Vladimir Sobolev's Books

Hörmander Spaces, Interpolation, and Elliptic Problems

By: Vladimir A. Mikhailets,Aleksandr A. Murach

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Hörmander Spaces, Interpolation, and Elliptic Problems

By: Vladimir A. Mikhailets,Aleksandr A. Murach

The monograph gives a detailed exposition of the theory of general elliptic operators (scalar and matrix) and elliptic boundary value problems in Hilbert scales of Hörmander function spaces. This theory was constructed by the authors in a number of papers published in 2005–2009. It is distinguished by a systematic use of the method of interpolation with a functional parameter of abstract Hilbert spaces and Sobolev inner product spaces. This method, the theory and their applications are expounded for the first time in the monographic literature. The monograph is written in detail and in a reader-friendly style. The complete proofs of theorems are given. This monograph is intended for a wide range of mathematicians whose research interests concern with mathematical analysis and differential equations.

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320

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110369060

ISBN 13

9783110369069

Differentiable Measures and the Malliavin Calculus

By: Vladimir Igorevich Bogachev

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Differentiable Measures and the Malliavin Calculus

By: Vladimir Igorevich Bogachev

This book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus--a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures. The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.

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506

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082184993X

ISBN 13

9780821849934

Elliptic Boundary Value Problems in Domains with Point Singularities

By: Vladimir Kozlov,V. A. Kozlov,V. G. Mazʹi︠a︡,Jürgen Rossmann

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Elliptic Boundary Value Problems in Domains with Point Singularities

By: Vladimir Kozlov,V. A. Kozlov,V. G. Mazʹi︠a︡,Jürgen Rossmann

For graduate students and research mathematicians interested in partial differential equations and who have a basic knowledge of functional analysis. Restricted to boundary value problems formed by differential operators, avoiding the use of pseudo- differential operators. Concentrates on fundamental results such as estimates for solutions in different function spaces, the Fredholm property of the problem's operator, regularity assertions, and asymptotic formulas for the solutions of near singular points. Considers the solutions in Sobolev spaces of both positive and negative orders. Annotation copyrighted by Book News, Inc., Portland, OR

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426

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821807544

ISBN 13

9780821807545

Methods of the Classical Theory of Elastodynamics

By: Vladimir B. Poruchikov

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Methods of the Classical Theory of Elastodynamics

By: Vladimir B. Poruchikov

Methods of the Classical Theory of Elastodynamics" deals not only with classical methods as developed in the past decades, but presents also very recent approaches. Applications and solutions to specific problems serve to illustrate the theoretical presentation. Keywords: Smirnov-Sobolev method with further developments; integral transforms; Wiener-Hopf technique; mixed boundary-value problems; time-dependent boundaries; solutions for unisotropic media (Willis method); 3-d dynamical problems for mixed boundary conditions.

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329

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642770991

ISBN 13

9783642770999

Differentiable Functions On Bad Domains

By: Vladimir G Maz'ya,Sergei Poborchi

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Differentiable Functions On Bad Domains

By: Vladimir G Maz'ya,Sergei Poborchi

The spaces of functions with derivatives in Lp, called the Sobolev spaces, play an important role in modern analysis. During the last decades, these spaces have been intensively studied and by now many problems associated with them have been solved. However, the theory of these function classes for domains with nonsmooth boundaries is still in an unsatisfactory state.In this book, which partially fills this gap, certain aspects of the theory of Sobolev spaces for domains with singularities are studied. We mainly focus on the so-called imbedding theorems, extension theorems and trace theorems that have numerous applications to partial differential equations. Some of such applications are given.Much attention is also paid to counter examples showing, in particular, the difference between Sobolev spaces of the first and higher orders. A considerable part of the monograph is devoted to Sobolev classes for parameter dependent domains and domains with cusps, which are the simplest non-Lipschitz domains frequently used in applications.This book will be interesting not only to specialists in analysis but also to postgraduate students.

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502

Publisher

World Scientific

Published Date

ISBN 10

9814498564

ISBN 13

9789814498562

Generalized Solutions of Operator Equations and Extreme Elements

By: D.A. Klyushin,S.I. Lyashko,D.A. Nomirovskii,Yu.I. Petunin,Vladimir Semenov

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Generalized Solutions of Operator Equations and Extreme Elements

By: D.A. Klyushin,S.I. Lyashko,D.A. Nomirovskii,Yu.I. Petunin,Vladimir Semenov

Abstract models for many problems in science and engineering take the form of an operator equation. The resolution of these problems often requires determining the existence and uniqueness of solutions to these equations. "Generalized Solutions of Operator Equations and Extreme Elements" presents recently obtained results in the study of the generalized solutions of operator equations and extreme elements in linear topological spaces. The presented results offer new methods of identifying these solutions and studying their properties. These new methods involve the application of a priori estimations and a general topological approach to construct generalized solutions of linear and nonlinear operator equations. The monograph is intended for mathematicians, graduate students and researchers studying functional analysis, operator theory, and the theory of optimal control.

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219

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461406196

ISBN 13

9781461406198

Gaussian Measures

By: Vladimir I. Bogachev

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Gaussian Measures

By: Vladimir I. Bogachev

This book gives a systematic exposition of the modern theory of Gaussian measures. It presents with complete and detailed proofs fundamental facts about finite and infinite dimensional Gaussian distributions. Covered topics include linear properties, convexity, linear and nonlinear transformations, and applications to Gaussian and diffusion processes. Suitable for use as a graduate text and/or a reference work, this volume contains many examples, exercises, and an extensive bibliography. It brings together many results that have not appeared previously in book form.

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450

Publisher

American Mathematical Soc.

Published Date

ISBN 10

147041869X

ISBN 13

9781470418694

Fokker–Planck–Kolmogorov Equations

By: Vladimir I. Bogachev,Nicolai V. Krylov,Michael Röckner,Stanislav V. Shaposhnikov

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Fokker–Planck–Kolmogorov Equations

By: Vladimir I. Bogachev,Nicolai V. Krylov,Michael Röckner,Stanislav V. Shaposhnikov

This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker–Planck–Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.

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495

Publisher

American Mathematical Society

Published Date

ISBN 10

1470470098

ISBN 13

9781470470098

Wavelet Theory

By: Igor Iakovlevič Novikov (mathématicien).),Vladimir I︠U︡rʹevich Protasov,Marii︠a︡ Aleksandrovna Skopina

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Wavelet Theory

By: Igor Iakovlevič Novikov (mathématicien).),Vladimir I︠U︡rʹevich Protasov,Marii︠a︡ Aleksandrovna Skopina

Wavelet theory lies on the crossroad of pure and computational mathematics, with connections to audio and video signal processing, data compression, and information transmission. The present book is devoted to a systematic exposition of modern wavelet theory. It details the construction of orthogonal and biorthogonal systems of wavelets and studies their structural and approximation properties, starting with basic theory and ending with special topics and problems. The book also presents some applications of wavelets. Historical commentary is supplied for each chapter in the book, and most chapters contain exercises. The book is intended for professional mathematicians and graduate students working in functional analysis and approximation theory. It is also useful for engineers applying wavelet theory in their work. Prerequisites for reading the book consist of graduate courses in real and functional analysis.

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522

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821849840

ISBN 13

9780821849842

The Nature and Models of Metamorphism

By: Vladimir V. Reverdatto,Igor I. Likhanov,Oleg P. Polyansky,Valentin S Sheplev,Vasiliy Yu Kolobov

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The Nature and Models of Metamorphism

By: Vladimir V. Reverdatto,Igor I. Likhanov,Oleg P. Polyansky,Valentin S Sheplev,Vasiliy Yu Kolobov

This book presents the genetic connections of metamorphism and geodynamics. It discusses the tectonic and magmatic processes as the reason of metamorphism, and the geological types of metamorphism, which define the features of Р-Т parameters and Р-Т-t paths. Three categories of metamorphism are distinguished depending on the heat flow rate: 1) at a geothermal gradient near to an average terrestrial ("normal") value; 2) at a heightened thermal gradient as the result of additional heat supply in the earth's crust by magmatic intrusions and diapirism of magma; 3) at a reduced thermal gradient during the collision of lithosphere plates and blocks of the earth's crust. The quantitative methods of description of metamorphism have been widely used in this book. The mathematical models of metamorphism have been studied in connection with magmatic intrusions, rifting process and magmatic diapirism. Mineral changes in the rocks controlled by variations of Р-Т of parameters, mass transfer and chemical reactions have also been characterized. The book proposes a quasi-stationary model of diffusion metasomatism with respect to the formation of zonal structures of minerals. The method of mineral thermobarometry for the conditions of unsteady equilibrium has been worked out; the quantitative analysis of mass transfer during metamorphic reactions in the rock matrix has been carried out, and the mobility of chemical elements at metamorphism has been estimated as well. The book is intended for specialists in the fields of petrology, mineralogy and geochemistry, and for students at the senior and graduate level.

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345

Publisher

Springer

Published Date

ISBN 10

3030030296

ISBN 13

9783030030292

Variational Theory of Splines

By: Anatoly Yu. Bezhaev,Vladimir A. Vasilenko

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Variational Theory of Splines

By: Anatoly Yu. Bezhaev,Vladimir A. Vasilenko

This book is a systematic description of the variational theory of splines in Hilbert spaces. All central aspects are discussed in the general form: existence, uniqueness, characterization via reproducing mappings and kernels, convergence, error estimations, vector and tensor hybrids in splines, dimensional reducing (traces of splines onto manifolds), etc. All considerations are illustrated by practical examples. In every case the numerical algorithms for the construction of splines are demonstrated.

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291

Publisher

Springer Science & Business Media

Published Date

ISBN 10

147573428X

ISBN 13

9781475734287

Spectroscopy of Low Temperature Plasma

By: Vladimir N. Ochkin

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Spectroscopy of Low Temperature Plasma

By: Vladimir N. Ochkin

Written by a distinguished plasma scientist and experienced author, this up-to-date work comprehensively covers current methods and new developments and techniques, including non-equilibrium atomic and molecular plasma states, as well as such new applications as gas lasers. Containing numerous appendices with reference data indispensable for plasma spectroscopy, such as statistical weights and partition sums and diatomic molecules. For plasmaphysicists, spectroscopists, materials scientists and physical chemists. Appendix H is only available online.

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630

Publisher

John Wiley & Sons

Published Date

ISBN 10

3527627510

ISBN 13

9783527627516

Nano and Micro Diamond Formation in Nature

Ultrafine Carbon Particles on Earth and Space

By: Sergei Simakov,Vittorio Scribano,Nikolai Melnik,Victor Pechnikov,Irina Drozdova,Vladimir Vyalov,Mikhail Novikov

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Nano and Micro Diamond Formation in Nature

Ultrafine Carbon Particles on Earth and Space

By: Sergei Simakov,Vittorio Scribano,Nikolai Melnik,Victor Pechnikov,Irina Drozdova,Vladimir Vyalov,Mikhail Novikov

In this book, readers will gain a deep understanding of the distinct characteristics and intricate formation mechanisms behind each type of diamond. A standout feature of this book is its in-depth exploration of nanodiamonds, shedding light on their unique formation processes. The narrative is thoughtfully organized, covering four main categories of natural diamonds and their related formation processes: 1)Interstellar nanodiamond particles; 2) Nano- and microcrustal diamonds associated with coals, sediments, and metamorphic rocks; 3) Nanodiamonds and microdiamonds associated with secondary alterations of mafic and ultramafic rocks mainly in the oceanic lithosphere; 4) Mantle-derived diamonds associated with kimberlites and their xenoliths, such as peridotites and eclogites. With clarity and precision, this book caters to both researchers and students in the fields of mineralogy and mineral formation. This book serves as an invaluable resource, offering an all-encompassing perspective on diamond formation, appealing to those curious minds eager to delve into the captivating realm of these precious gems.

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136

Publisher

Springer Nature

Published Date

ISBN 10

3031432789

ISBN 13

9783031432781

Moduli in Modern Mapping Theory

By: Olli Martio,Vladimir Ryazanov,Uri Srebro,Eduard Yakubov

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Moduli in Modern Mapping Theory

By: Olli Martio,Vladimir Ryazanov,Uri Srebro,Eduard Yakubov

Based on recent research papers, this book presents a modern account of mapping theory with emphasis on quasiconformal mapping and its generalizations. It contains an extensive bibliography.

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368

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Springer Science & Business Media

Published Date

ISBN 10

0387855882

ISBN 13

9780387855882

Jacques Hadamard

A Universal Mathematician

By: Vladimir Gilelevič Mazʹâ,T. O. Shaposhnikova

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Jacques Hadamard

A Universal Mathematician

By: Vladimir Gilelevič Mazʹâ,T. O. Shaposhnikova

This book presents a fascinating story of the long life and great accomplishments of Jacques Hadamard (1865-1963), who was once called 'the living legend of mathematics'. As one of the last universal mathematicians, Hadamard's contributions to mathematics are landmarks in various fields. His life is linked with world history of the 20th century in a dramatic way. This work provides an inspiring view of the development of various branches of mathematics during the 19th and 20th centuries.Part I of the book portrays Hadamard's family, childhood and student years, scientific triumphs, and his personal life and trials during the first two world wars. The story is told of his involvement in the Dreyfus affair and his subsequent fight for justice and human rights. Also recounted are Hadamard's worldwide travels, his famous seminar, his passion for botany, his home orchestra, where he played the violin with Einstein, and his interest in the psychology of mathematical creativity. Hadamard's life is described in a readable and inviting way.The authors humorously weave throughout the text his jokes and the myths about him. They also movingly recount the tragic side of his life. Stories about his relatives and friends, and old letters and documents create an authentic and colorful picture. The book contains over 300 photographs and illustrations. Part II of the book includes a lucid overview of Hadamard's enormous work, spanning over six decades. The authors do an excellent job of connecting his results to current concerns.While the book is accessible to beginners, it also provides rich information of interest to experts. Vladimir Mazya and Tatyana Shaposhnikova were the 2003 laureates of the Insitut de France's Prix Alfred Verdaguer. One or more prizes are awarded each year, based on suggestions from the Academie francaise, the Academie de sciences, and the Academie de beaux-arts, for the most remarkable work in the arts, literature, and the sciences. In 2003, the award for excellence was granted in recognition of Mazya and Shaposhnikova's book, ""Jacques Hadamard, A Universal Mathematician"", which is both an historical book about a great citizen and a scientific book about a great mathematician.

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604

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821819232

ISBN 13

9780821819234

Quantization Methods in the Theory of Differential Equations

By: Vladimir E. Nazaikinskii,B.-W. Schulze,Boris Yu. Sternin

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Quantization Methods in the Theory of Differential Equations

By: Vladimir E. Nazaikinskii,B.-W. Schulze,Boris Yu. Sternin

This volume presents a systematic and mathematically rigorous exposition of methods for studying linear partial differential equations. It focuses on quantization of the corresponding objects (states, observables and canonical transformations) in the phase space. The quantization of all three types of classical objects is carried out in a unified w

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369

Publisher

CRC Press

Published Date

ISBN 10

1482265036

ISBN 13

9781482265033

Elliptic Theory on Singular Manifolds

By: Vladimir E. Nazaikinskii,Anton Yu. Savin,Bert-Wolfgang Schulze,Boris Yu. Sternin

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Elliptic Theory on Singular Manifolds

By: Vladimir E. Nazaikinskii,Anton Yu. Savin,Bert-Wolfgang Schulze,Boris Yu. Sternin

The analysis and topology of elliptic operators on manifolds with singularities are much more complicated than in the smooth case and require completely new mathematical notions and theories. While there has recently been much progress in the field, many of these results have remained scattered in journals and preprints. Starting from an ele

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372

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CRC Press

Published Date

ISBN 10

1420034979

ISBN 13

9781420034974

Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations

By: Vladimir Kozlov,V. G. Mazʹi︠a︡,Jürgen Rossmann

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Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations

By: Vladimir Kozlov,V. G. Mazʹi︠a︡,Jürgen Rossmann

This book focuses on the analysis of eigenvalues and eigenfunctions that describe singularities of solutions to elliptic boundary value problems in domains with corners and edges. The authors treat both classical problems of mathematical physics and general elliptic boundary value problems. The volume is divided into two parts: The first is devoted to the power-logarithmic singularities of solutions to classical boundary value problems of mathematical physics. The second deals with similar singularities for higher order elliptic equations and systems. Chapter 1 collects basic facts concerning operator pencils acting in a pair of Hilbert spaces. Related properties of ordinary differential equations with constant operator coefficients are discussed and connections with the theory of general elliptic boundary value problems in domains with conic vertices are outlined. New results are presented. Chapter 2 treats the Laplace operator as a starting point and a model for the subsequent study of angular and conic singularities of solutions. Chapter 3 considers the Dirichlet boundary condition beginning with the plane case and turning to the space problems. Chapter 4 investigates some mixed boundary conditions. The Stokes system is discussed in Chapters 5 and 6, and Chapter 7 concludes with the Dirichlet problem for the polyharmonic operator. Chapter 8 studies the Dirichlet problem for general elliptic differential equations of order 2m in an angle. In Chapter 9, an asymptotic formula for the distribution of eigenvalues of operator pencils corresponding to general elliptic boundary value problems in an angle is obtained. Chapters 10 and 11 discuss the Dirichlet problem for elliptic systems of differential equations of order 2 in an n-dimensional cone. Chapter 12 studies the Neumann problem for general elliptic systems, in particular with eigenvalues of the corresponding operator pencil in the strip $\mid {\Re} \lambda - m + /2n \mid \leq 1/2$. It is shown that only integer numbers contained in this strip are eigenvalues. Applications are placed within chapter introductions and as special sections at the end of chapters. Prerequisites include standard PDE and functional analysis courses.

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449

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821827278

ISBN 13

9780821827277

Global Climatology and Ecodynamics

Anthropogenic Changes to Planet Earth

By: Arthur Philip Cracknell,Vladimir F. Krapivin

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Global Climatology and Ecodynamics

Anthropogenic Changes to Planet Earth

By: Arthur Philip Cracknell,Vladimir F. Krapivin

The exclusive role of natural ecosystems is a key factor in the maintenance of the biospheric equilibrium. The current global crisis is largely caused by their dramatic decline by 43% in the past hundred years. Ignoring the immutable laws and limitations which determine the existence of all living things in the biosphere could lead humanity to an ecological catastrophe. This book presents the ecological, demographic, economic and socio-psychological manifestations of the global crisis and outlines the immutable laws and limitations which determine the existence of all living things in the biosphere. The authors are eminently qualified to write about the problems associated with the global crisis and consider the causes behind humanity's conflict with its environment. V. Danilov-Danilian, Associate of the Russian Academy of Sciences and Russia's former Minister of the Environment, and K. Losev, professor at Moscow State university, are leading Russian ecologists and I. Reyf is a journalist who specializes in ecology and global development. Dr. Danilov-Danilian works on the economics of nature management, economic and mathematical model building, sustainable development theory and ecology. Dr Losev is the chief researcher and head of the division of the VINITI. All the authors have published numerous papers, articles and books on such subjects as glaciology, hydrology, environment studies, global change and sustainable development.

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541

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Springer Science & Business Media

Published Date

ISBN 10

3540782095

ISBN 13

9783540782094

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains

Volume I

By: Vladimir Maz'ya,Serguei Nazarov,Boris Plamenevskij

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Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains

Volume I

By: Vladimir Maz'ya,Serguei Nazarov,Boris Plamenevskij

For the first time in the mathematical literature, this two-volume work introduces a unified and general approach to the subject. To a large extent, the book is based on the authors’ work, and has no significant overlap with other books on the theory of elliptic boundary value problems.

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448

Publisher

Birkhäuser

Published Date

ISBN 10

3034884346

ISBN 13

9783034884341

Homogenization of Partial Differential Equations

By: Vladimir A. Marchenko,Evgueni Ya. Khruslov

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Homogenization of Partial Differential Equations

By: Vladimir A. Marchenko,Evgueni Ya. Khruslov

A comprehensive study of homogenized problems, focusing on the construction of nonstandard models Details a method for modeling processes in microinhomogeneous media (radiophysics, filtration theory, rheology, elasticity theory, and other domains) Complete proofs of all main results, numerous examples Classroom text or comprehensive reference for graduate students, applied mathematicians, physicists, and engineers

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407

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Springer Science & Business Media

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ISBN 10

0817644687

ISBN 13

9780817644680

The Radiation Legacy of the Soviet Nuclear Complex

An Analytical Overview

By: Nikolai N. Egorov,Vladimir M. Novikov,Frank L. Parker,Victor K. Popov

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The Radiation Legacy of the Soviet Nuclear Complex

An Analytical Overview

By: Nikolai N. Egorov,Vladimir M. Novikov,Frank L. Parker,Victor K. Popov

A study of the legacy of nuclear contamination in the Soviet Union. It gives the location and characteristics of the accumulated radioactive material and wastes by each sector, from ore and mining to use and disposal. It describes types of storage, capacity and utilization, age and location. It gives information on the territories and locations contaminated, by normal operations and by accidents, from which strategic plans for remediation can be formulated.

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277

Publisher

Routledge

Published Date

ISBN 10

1134197144

ISBN 13

9781134197149

Greedy Approximation

By: Vladimir Temlyakov

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Greedy Approximation

By: Vladimir Temlyakov

This first book on greedy approximation gives a systematic presentation of the fundamental results. It also contains an introduction to two hot topics in numerical mathematics: learning theory and compressed sensing. Nonlinear approximation is becoming increasingly important, especially since two types are frequently employed in applications: adaptive methods are used in PDE solvers, while m-term approximation is used in image/signal/data processing, as well as in the design of neural networks. The fundamental question of nonlinear approximation is how to devise good constructive methods (algorithms) and recent results have established that greedy type algorithms may be the solution. The author has drawn on his own teaching experience to write a book ideally suited to graduate courses. The reader does not require a broad background to understand the material. Important open problems are included to give students and professionals alike ideas for further research.

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433

Publisher

Cambridge University Press

Published Date

ISBN 10

1139502808

ISBN 13

9781139502801

Vector-Valued Partial Differential Equations and Applications

Cetraro, Italy 2013

By: Bernard Dacorogna,Nicola Fusco,Stefan Müller,Vladimir Sverak

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Vector-Valued Partial Differential Equations and Applications

Cetraro, Italy 2013

By: Bernard Dacorogna,Nicola Fusco,Stefan Müller,Vladimir Sverak

Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard Dacorogna), The stability of the isoperimetric inequality (Nicola Fusco), Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities (Stefan Müller), and Aspects of PDEs related to fluid flows (Vladimir Sverák). These lectures are addressed to graduate students and researchers in the field.

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256

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Springer

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ISBN 10

3319545140

ISBN 13

9783319545141

Game-Theoretic Foundations for Probability and Finance

By: Glenn Shafer,Vladimir Vovk

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Game-Theoretic Foundations for Probability and Finance

By: Glenn Shafer,Vladimir Vovk

Game-theoretic probability and finance come of age Glenn Shafer and Vladimir Vovk’s Probability and Finance, published in 2001, showed that perfect-information games can be used to define mathematical probability. Based on fifteen years of further research, Game-Theoretic Foundations for Probability and Finance presents a mature view of the foundational role game theory can play. Its account of probability theory opens the way to new methods of prediction and testing and makes many statistical methods more transparent and widely usable. Its contributions to finance theory include purely game-theoretic accounts of Ito’s stochastic calculus, the capital asset pricing model, the equity premium, and portfolio theory. Game-Theoretic Foundations for Probability and Finance is a book of research. It is also a teaching resource. Each chapter is supplemented with carefully designed exercises and notes relating the new theory to its historical context. Praise from early readers “Ever since Kolmogorov's Grundbegriffe, the standard mathematical treatment of probability theory has been measure-theoretic. In this ground-breaking work, Shafer and Vovk give a game-theoretic foundation instead. While being just as rigorous, the game-theoretic approach allows for vast and useful generalizations of classical measure-theoretic results, while also giving rise to new, radical ideas for prediction, statistics and mathematical finance without stochastic assumptions. The authors set out their theory in great detail, resulting in what is definitely one of the most important books on the foundations of probability to have appeared in the last few decades.” – Peter Grünwald, CWI and University of Leiden “Shafer and Vovk have thoroughly re-written their 2001 book on the game-theoretic foundations for probability and for finance. They have included an account of the tremendous growth that has occurred since, in the game-theoretic and pathwise approaches to stochastic analysis and in their applications to continuous-time finance. This new book will undoubtedly spur a better understanding of the foundations of these very important fields, and we should all be grateful to its authors.” – Ioannis Karatzas, Columbia University

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554

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John Wiley & Sons

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ISBN 10

1118548027

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9781118548028

Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains

By: Michail Borsuk,Vladimir Kondratiev

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Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains

By: Michail Borsuk,Vladimir Kondratiev

The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points.Key features:* New the Hardy – Friedrichs – Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation.* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m – Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.

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538

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Elsevier

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ISBN 10

0080461735

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9780080461731

Lectures on Functional Analysis and Applications

By: Vladimir Semenovich Pugachev,Igor? Nikolaevich Sinit?s?yn

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Lectures on Functional Analysis and Applications

By: Vladimir Semenovich Pugachev,Igor? Nikolaevich Sinit?s?yn

This book is intended for those having only a moderate background in mathematics, who need to increase their mathematical knowledge for development in their areas of work and to read the related mathematical literature. The material covered, which includes practically all the information on functional analysis that may be necessary for those working in various areas of applications of mathematics, as well as the simplicity of presentation, differentiates this book from others. About 300 examples and more than 500 problems are provided to help readers understand and master the theories presented. The list of references enables readers to explore those topics in which they are interested, and gather further information about applications used as examples in the book.Applications: Probability Theory and Statistics, Signal and Image Processing, Systems Analysis and Design.

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756

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World Scientific

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ISBN 10

9810237235

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9789810237233

Hyperbolic Cross Approximation

By: Dinh Dũng,Vladimir Temlyakov,Tino Ullrich

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Hyperbolic Cross Approximation

By: Dinh Dũng,Vladimir Temlyakov,Tino Ullrich

This book provides a systematic survey of classical and recent results on hyperbolic cross approximation. Motivated by numerous applications, the last two decades have seen great success in studying multivariate approximation. Multivariate problems have proven to be considerably more difficult than their univariate counterparts, and recent findings have established that multivariate mixed smoothness classes play a fundamental role in high-dimensional approximation. The book presents essential findings on and discussions of linear and nonlinear approximations of the mixed smoothness classes. Many of the important open problems explored here will provide both students and professionals with inspirations for further research.

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222

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Springer

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ISBN 10

3319922408

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9783319922409

C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians

By: Werner O. Amrein,Anne Boutet de Monvel,Vladimir Georgescu

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C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians

By: Werner O. Amrein,Anne Boutet de Monvel,Vladimir Georgescu

The conjugate operator method is a powerful recently developed technique for studying spectral properties of self-adjoint operators. One of the purposes of this volume is to present a refinement of the original method due to Mourre leading to essentially optimal results in situations as varied as ordinary differential operators, pseudo-differential operators and N-body Schrödinger hamiltonians. Another topic is a new algebraic framework for the N-body problem allowing a simple and systematic treatment of large classes of many-channel hamiltonians. The monograph will be of interest to research mathematicians and mathematical physicists. The authors have made efforts to produce an essentially self-contained text, which makes it accessible to advanced students. Thus about one third of the book is devoted to the development of tools from functional analysis, in particular real interpolation theory for Banach spaces and functional calculus and Besov spaces associated with multi-parameter C0-groups. Certainly this monograph (containing a bibliography of 170 items) is a well-written contribution to this field which is suitable to stimulate further evolution of the theory. (Mathematical Reviews)

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469

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Springer Science & Business Media

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ISBN 10

3034807333

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9783034807333

Differential Equations with Operator Coefficients

with Applications to Boundary Value Problems for Partial Differential Equations

By: Vladimir Kozlov,Vladimir Maz'ya

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Differential Equations with Operator Coefficients

with Applications to Boundary Value Problems for Partial Differential Equations

By: Vladimir Kozlov,Vladimir Maz'ya

The first systematic, self-contained presentation of a theory of arbitrary order ODEs with unbounded operator coefficients in a Hilbert or Banach space. Developed over the last 10 years by the authors, it deals with conditions of solvability, classes of uniqueness, estimates for solutions and asymptotic representations of solutions at infinity.

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449

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Springer Science & Business Media

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ISBN 10

3662115557

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9783662115558

Measure Theory

By: Vladimir I. Bogachev

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Measure Theory

By: Vladimir I. Bogachev

This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.

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1075

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Springer Science & Business Media

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ISBN 10

3540345140

ISBN 13

9783540345145

Real and Functional Analysis

By: Vladimir I. Bogachev,Oleg G. Smolyanov

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Real and Functional Analysis

By: Vladimir I. Bogachev,Oleg G. Smolyanov

This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.

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602

Publisher

Springer Nature

Published Date

ISBN 10

3030382192

ISBN 13

9783030382193

Topological Methods in Hydrodynamics

By: Vladimir I. Arnold,Boris A. Khesin

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Topological Methods in Hydrodynamics

By: Vladimir I. Arnold,Boris A. Khesin

The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.

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376

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Springer Science & Business Media

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ISBN 10

0387225897

ISBN 13

9780387225890

The Beltrami Equation

A Geometric Approach

By: Vladimir Gutlyanskii,Vladimir Ryazanov,Uri Srebro,Eduard Yakubov

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The Beltrami Equation

A Geometric Approach

By: Vladimir Gutlyanskii,Vladimir Ryazanov,Uri Srebro,Eduard Yakubov

This book is devoted to the Beltrami equations that play a significant role in Geometry, Analysis and Physics and, in particular, in the study of quasiconformal mappings and their generalizations, Riemann surfaces, Kleinian groups, Teichmuller spaces, Clifford analysis, meromorphic functions, low dimensional topology, holomorphic motions, complex dynamics, potential theory, electrostatics, magnetostatics, hydrodynamics and magneto-hydrodynamics. The purpose of this book is to present the recent developments in the theory of Beltrami equations; especially those concerning degenerate and alternating Beltrami equations. The authors study a wide circle of problems like convergence, existence, uniqueness, representation, removal of singularities, local distortion estimates and boundary behavior of solutions to the Beltrami equations. The monograph contains a number of new types of criteria in the given problems, particularly new integral conditions for the existence of regular solutions to the Beltrami equations that turned out to be not only sufficient but also necessary. The most important feature of this book concerns the unified geometric approach based on the modulus method that is effectively applied to solving the mentioned problems. Moreover, it is characteristic for the book application of many new concepts as strong ring solutions, tangent dilatations, weakly flat and strongly accessible boundaries, functions of finite mean oscillations and new integral conditions that make possible to realize a more deep and refined analysis of problems related to the Beltrami equations. Mastering and using these new tools also gives essential advantages for the reader in the research of modern problems in many other domains. Every mathematics graduate library should have a copy of this book.

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309

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Springer Science & Business Media

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ISBN 10

1461431913

ISBN 13

9781461431916

Structural Properties of Porous Materials and Powders Used in Different Fields of Science and Technology

By: Yury Mironovich Volfkovich,Anatoly Nikolaevich Filippov,Vladimir Sergeevich Bagotsky

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Structural Properties of Porous Materials and Powders Used in Different Fields of Science and Technology

By: Yury Mironovich Volfkovich,Anatoly Nikolaevich Filippov,Vladimir Sergeevich Bagotsky

This book provides a comprehensive and concise description of most important aspects of experimental and theoretical investigations of porous materials and powders, with the use and application of these materials in different fields of science, technology, national economy and environment. It allows the reader to understand the basic regularities of heat and mass transfer and adsorption occurring in qualitatively different porous materials and products, and allows the reader to optimize the functional properties of porous and powdered products and materials. Written in an straightforward and transparent manner, this book is accessible to both experts and those without specialist knowledge, and it is further elucidated by drawings, schemes and photographs. Porous materials and powders with different pore sizes are used in many areas of industry, geology, agriculture and science. These areas include (i) a variety of devices and supplies; (ii) thermal insulation and building materials; (iii) oil-bearing geological, gas-bearing and water-bearing rocks; and (iv) biological objects. Structural Properties of Porous Materials and Powders Used in Different Fields of Science and Technology is intended for a wide-ranging audience specializing in different fields of science and engineering including engineers, geologists, geophysicists, oil and gas producers, agronomists, physiologists, pharmacists, researchers, teachers and students.

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331

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Springer

Published Date

ISBN 10

144716377X

ISBN 13

9781447163770

Mathematical Understanding of Nature

Essays on Amazing Physical Phenomena and Their Understanding by Mathematicians

By: Vladimir Igorevich Arnolʹd

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Mathematical Understanding of Nature

Essays on Amazing Physical Phenomena and Their Understanding by Mathematicians

By: Vladimir Igorevich Arnolʹd

This collection of 39 short stories gives the reader a unique opportunity to take a look at the scientific philosophy of Vladimir Arnold, one of the most original contemporary researchers. Topics of the stories included range from astronomy, to mirages, to motion of glaciers, to geometry of mirrors and beyond. In each case Arnold's explanation is both deep and simple, which makes the book interesting and accessible to an extremely broad readership. Original illustrations hand drawn by the author help the reader to further understand and appreciate Arnold's view on the relationship between mathematics and science."--

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184

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470418894

ISBN 13

9781470418892

Elliptic Theory and Noncommutative Geometry

Nonlocal Elliptic Operators

By: Vladimir E. Nazaykinskiy,A. Yu. Savin,B. Yu. Sternin

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Elliptic Theory and Noncommutative Geometry

Nonlocal Elliptic Operators

By: Vladimir E. Nazaykinskiy,A. Yu. Savin,B. Yu. Sternin

This comprehensive yet concise book deals with nonlocal elliptic differential operators. These are operators whose coefficients involve shifts generated by diffeomorphisms of the manifold on which the operators are defined. This is the first book featuring a consistent application of methods of noncommutative geometry to the index problem in the theory of nonlocal elliptic operators. To make the book self-contained, the authors have included necessary geometric material.

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224

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Springer Science & Business Media

Published Date

ISBN 10

3764387750

ISBN 13

9783764387754

The Localization Problem in Index Theory of Elliptic Operators

By: Vladimir Nazaikinskii,Bert-Wolfgang Schulze,Boris Sternin

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The Localization Problem in Index Theory of Elliptic Operators

By: Vladimir Nazaikinskii,Bert-Wolfgang Schulze,Boris Sternin

The book deals with the localization approach to the index problem for elliptic operators. Localization ideas have been widely used for solving various specific index problems for a long time, but the fact that there is actually a fundamental localization principle underlying all these solutions has mostly passed unnoticed. The ignorance of this general principle has often necessitated using various artificial tricks and hindered the solution of new important problems in index theory. So far, the localization principle has been only scarcely covered in journal papers and not covered at all in monographs. The suggested book is intended to fill the gap. So far, it is the first and only monograph dealing with the topic. Both the general localization principle and its applications to specific problems, existing and new, are covered. The book will be of interest to working mathematicians as well as graduate and postgraduate university students specializing in differential equations and related topics.

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Page Count

122

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Springer Science & Business Media

Published Date

ISBN 10

3034805101

ISBN 13

9783034805100

Book's by Vladimir Sobolev

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