Boris Sternin's Books

Differential Equations on Complex Manifolds

By: Boris Sternin,Victor Shatalov

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Differential Equations on Complex Manifolds

By: Boris Sternin,Victor Shatalov

The present monograph is devoted to the complex theory of differential equations. Not yet a handbook, neither a simple collection of articles, the book is a first attempt to present a more or less detailed exposition of a young but promising branch of mathematics, that is, the complex theory of partial differential equations. Let us try to describe the framework of this theory. First, simple examples show that solutions of differential equations are, as a rule, ramifying analytic functions. and, hence, are not regular near points of their ramification. Second, bearing in mind these important properties of solutions, we shall try to describe the method solving our problem. Surely, one has first to consider differential equations with constant coefficients. The apparatus solving such problems is well-known in the real the ory of differential equations: this is the Fourier transformation. Un fortunately, such a transformation had not yet been constructed for complex-analytic functions and the authors had to construct by them selves. This transformation is, of course, the key notion of the whole theory.

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517

Publisher

Springer Science & Business Media

Published Date

ISBN 10

940171259X

ISBN 13

9789401712590

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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122

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Springer Science & Business Media

Published Date

ISBN 10

3034805101

ISBN 13

9783034805100

Introduction to Complex Theory of Differential Equations

By: Anton Savin,Boris Sternin

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Introduction to Complex Theory of Differential Equations

By: Anton Savin,Boris Sternin

This book discusses the complex theory of differential equations or more precisely, the theory of differential equations on complex-analytic manifolds. Although the theory of differential equations on real manifolds is well known – it is described in thousands of papers and its usefulness requires no comments or explanations – to date specialists on differential equations have not focused on the complex theory of partial differential equations. However, as well as being remarkably beautiful, this theory can be used to solve a number of problems in real theory, for instance, the Poincaré balayage problem and the mother body problem in geophysics. The monograph does not require readers to be familiar with advanced notions in complex analysis, differential equations, or topology. With its numerous examples and exercises, it appeals to advanced undergraduate and graduate students, and also to researchers wanting to familiarize themselves with the subject.

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142

Publisher

Birkhäuser

Published Date

ISBN 10

3319517449

ISBN 13

9783319517445

Methods of Noncommutative Analysis

Theory and Applications

By: Vladimir E. Nazaikinskii,Victor E. Shatalov,Boris Yu. Sternin

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Methods of Noncommutative Analysis

Theory and Applications

By: Vladimir E. Nazaikinskii,Victor E. Shatalov,Boris Yu. Sternin

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic Models for Fractional Calculus, second edition (2018) Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Kezheng Li, Group Schemes and Their Actions (2019; together with Tsinghua University Press) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)

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385

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110813548

ISBN 13

9783110813548

Borel-Laplace Transform and Asymptotic Theory

Introduction to Resurgent Analysis

By: Boris Yu. Sternin,Victor E. Shatalov

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Borel-Laplace Transform and Asymptotic Theory

Introduction to Resurgent Analysis

By: Boris Yu. Sternin,Victor E. Shatalov

The resurgent function theory introduced by J. Ecalle is one of the most interesting theories in mathematical analysis. In essence, the theory provides a resummation method for divergent power series (e.g., asymptotic series), and allows this method to be applied to mathematical problems. This new book introduces the methods and ideas inherent in resurgent analysis. The discussions are clear and precise, and the authors assume no previous knowledge of the subject. With this new book, mathematicians and other scientists can acquaint themselves with an interesting and powerful branch of asymptotic theory - the resurgent functions theory - and will learn techniques for applying it to solve problems in mathematics and mathematical sciences.

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284

Publisher

CRC Press

Published Date

ISBN 10

084939435X

ISBN 13

9780849394355

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

Publisher

CRC Press

Published Date

ISBN 10

1420034979

ISBN 13

9781420034974

Electromagnetic Fields

Restrictions and Approximation

By: Boris Z. Katsenelenbaum

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Electromagnetic Fields

Restrictions and Approximation

By: Boris Z. Katsenelenbaum

The fields scattered by metallic bodies or radiated by some types of antennas are created by the surfaces currents and therefore they are subject to some restrictions. The book is the first one where the properties of these fields are investigated in details. The properties have the important significance for the antenna synthesis, body shape reconstruction and other diffraction problems. The material of the book lies in the meetingpoint of the antenna theory, highfrequency electrodynamics and inverse scattering problems. The author is an internationally renowned investigator in the field of electromagnetic waves and diffraction theory.

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Page Count

236

Publisher

John Wiley & Sons

Published Date

ISBN 10

352762208X

ISBN 13

9783527622085

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II

Volume II

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

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Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II

Volume II

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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Page Count

336

Publisher

Birkhäuser

Published Date

ISBN 10

303488432X

ISBN 13

9783034884327

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 Problems in Domains with Piecewise Smooth Boundaries

By: Sergey Nazarov,Boris A. Plamenevsky

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Elliptic Problems in Domains with Piecewise Smooth Boundaries

By: Sergey Nazarov,Boris A. Plamenevsky

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537

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110848910

ISBN 13

9783110848915

Conformal Geometry of Discrete Groups and Manifolds

By: Boris N. Apanasov

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Conformal Geometry of Discrete Groups and Manifolds

By: Boris N. Apanasov

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

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541

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110808056

ISBN 13

9783110808056

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

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448

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Birkhäuser

Published Date

ISBN 10

3034884346

ISBN 13

9783034884341

Introduction to Complex Theory of Differential Equations

By: Anton Savin,Boris Sternin

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Introduction to Complex Theory of Differential Equations

By: Anton Savin,Boris Sternin

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142

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Birkhäuser

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ISBN 10

3319517449

ISBN 13

9783319517445

Lagrangian Manifolds and the Maslov Operator

By: Aleksandr S. Mishchenko,Viktor E. Shatalov,Boris Sternin

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Lagrangian Manifolds and the Maslov Operator

By: Aleksandr S. Mishchenko,Viktor E. Shatalov,Boris Sternin

This book presents Maslov's canonical operator method for finding asymptotic solutions of pseudo differential equations. The classical WKB method, so named in honor of its authors: Wentzel, Kramers and Brillouin, was created for finding quasi classical approximations in quantum mechanics. The simplicity, obviousness and "physicalness" of this method quickly made it popular: specialists in mathematical physics accepted it unequivocally as one of the weapons in their arsenal. The number of publications which are connected with the WKB method in one way or another can probably no longer be counted. The alternative name of the WKB method in diffraction problem- the ray method or the method of geometric optics - indicates that the approximations in the WKB method are constructed by means of rays. More precisely, the first approximation of the WKB method is constructed by means of rays (isolating the singular part), after which the usual methods of the (regular) theory of perturbations are applied. However, the ray method is not applicable at the points of space where the rays focus or form a caustic. Mathematically this fact expresses itself in the fact that the amplitude of the waves at such points become infinite.

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395

Publisher

Springer

Published Date

ISBN 10

3540136134

ISBN 13

9783540136132

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

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122

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Springer Science & Business Media

Published Date

ISBN 10

3034805101

ISBN 13

9783034805100

Contact Geometry and Linear Differential Equations

By: Vladimir E. Nazaikinskii,Victor E. Shatalov,Boris Yu. Sternin

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Contact Geometry and Linear Differential Equations

By: Vladimir E. Nazaikinskii,Victor E. Shatalov,Boris Yu. Sternin

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

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