Alexander Koldobsky's Books

The Interface Between Convex Geometry and Harmonic Analysis

By: Alexander Koldobsky,Vladyslav Yaskin

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The Interface Between Convex Geometry and Harmonic Analysis

By: Alexander Koldobsky,Vladyslav Yaskin

The book is written in the form of lectures accessible to graduate students. This approach allows the reader to clearly see the main ideas behind the method, rather than to dwell on technical difficulties. The book also contains discussions of the most recent advances in the subject. The first section of each lecture is a snapshot of that lecture. By reading each of these sections first, novices can gain an overview of the subject, then return to the full text for more details."--BOOK JACKET.

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Page Count

128

Publisher

American Mathematical Soc.

ISBN 10

0821883356

ISBN 13

9780821883358

Fourier Analysis in Convex Geometry

By: Alexander Koldobsky

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Fourier Analysis in Convex Geometry

By: Alexander Koldobsky

The study of the geometry of convex bodies based on information about sections and projections of these bodies has important applications in many areas of mathematics and science. In this book, a new Fourier analysis approach is discussed. The idea is to express certain geometric properties of bodies in terms of Fourier analysis and to use harmonic analysis methods to solve geometric problems. One of the results discussed in the book is Ball's theorem, establishing the exact upper bound for the -dimensional volume of hyperplane sections of the -dimensional unit cube (it is for each ). Another is the Busemann-Petty problem: if and are two convex origin-symmetric -dimensional bodies and the -dimensional volume of each central hyperplane section of is less than the -dimensional volume of the corresponding section of , is it true that the -dimensional volume of is less than the volume of ? (The answer is positive for and negative for .) The book is suitable for graduate students and researchers interested in geometry, harmonic and functional analysis, and probability. Prerequisites for reading this book include basic real, complex, and functional analysis.

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Page Count

178

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470419521

ISBN 13

9781470419523

Yangians and Classical Lie Algebras

By: Alexander Molev

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Yangians and Classical Lie Algebras

By: Alexander Molev

The Yangians and twisted Yangians are remarkable associative algebras taking their origins from the work of St. Petersburg's school of mathematical physics in the 1980s. This book is an introduction to the theory of Yangians and twisted Yangians, with a particular emphasis on the relationship with the classical matrix Lie algebras.

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Page Count

422

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821843745

ISBN 13

9780821843741

Innovations and New Technologies (v.2)

By: Alexander Bolonkin

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Innovations and New Technologies (v.2)

By: Alexander Bolonkin

In recent years of the 21st Century the author of this book and other scientists as well, have instigated and described many new ideas, researches, theories, macro-projects, USA and other countries patented concepts, speculative macro-engineering ideas, projects and other general innovations in technology and environment change. In aerospace these include air catapult transportation, hypersonic ground electric AB engine, protection of the Earth from asteroids and delivery of asteroids to the Earth, re-entry space apparatus to Earth, airborne wind turbines, electronic wind generator and propulsion, long distance shells, new self-propelled penetration bomb, inexpensive mini thermonuclear reactor, etc. In technology these include new ideas and innovation in space sciences and Earth technologies: Underground explosion nuclear energy; Electron hydro electric generator; Electron super speed hydro propulsion; Electric theory of tornado; Protection from tornado; and so on.

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Page Count

450

Publisher

Lulu.com

Published Date

ISBN 10

1312622806

ISBN 13

9781312622807

Painlevé Transcendents

The Riemann-Hilbert Approach

By: Athanassios S. Fokas,Alexander R. Its,Andrei A. Kapaev,Victor Yu. Novokshenov

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Painlevé Transcendents

The Riemann-Hilbert Approach

By: Athanassios S. Fokas,Alexander R. Its,Andrei A. Kapaev,Victor Yu. Novokshenov

At the turn of the twentieth century, the French mathematician Paul Painlevé and his students classified second order nonlinear ordinary differential equations with the property that the location of possible branch points and essential singularities of their solutions does not depend on initial conditions. It turned out that there are only six such equations (up to natural equivalence), which later became known as Painlevé I–VI. Although these equations were initially obtained answering a strictly mathematical question, they appeared later in an astonishing (and growing) range of applications, including, e.g., statistical physics, fluid mechanics, random matrices, and orthogonal polynomials. Actually, it is now becoming clear that the Painlevé transcendents (i.e., the solutions of the Painlevé equations) play the same role in nonlinear mathematical physics that the classical special functions, such as Airy and Bessel functions, play in linear physics. The explicit formulas relating the asymptotic behaviour of the classical special functions at different critical points play a crucial role in the applications of these functions. It is shown in this book that even though the six Painlevé equations are nonlinear, it is still possible, using a new technique called the Riemann-Hilbert formalism, to obtain analogous explicit formulas for the Painlevé transcendents. This striking fact, apparently unknown to Painlevé and his contemporaries, is the key ingredient for the remarkable applicability of these “nonlinear special functions”. The book describes in detail the Riemann-Hilbert method and emphasizes its close connection to classical monodromy theory of linear equations as well as to modern theory of integrable systems. In addition, the book contains an ample collection of material concerning the asymptotics of the Painlevé functions and their various applications, which makes it a good reference source for everyone working in the theory and applications of Painlevé equations and related areas.

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Page Count

570

Publisher

American Mathematical Society

Published Date

ISBN 10

1470475561

ISBN 13

9781470475567

The Interface Between Convex Geometry and Harmonic Analysis

By: Alexander Koldobsky,Vladyslav Yaskin

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The Interface Between Convex Geometry and Harmonic Analysis

By: Alexander Koldobsky,Vladyslav Yaskin

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Solve jigsaw puzzle

Age

Page Count

128

Publisher

American Mathematical Soc.

ISBN 10

0821883356

ISBN 13

9780821883358

Fourier Analysis in Convex Geometry

By: Alexander Koldobsky

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Fourier Analysis in Convex Geometry

By: Alexander Koldobsky

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Solve jigsaw puzzle

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Page Count

178

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470419521

ISBN 13

9781470419523

Book's by Alexander Koldobsky

The Interface Between Convex Geometry and Harmonic Analysis

The Interface Between Convex Geometry and Harmonic Analysis

Fourier Analysis in Convex Geometry

Fourier Analysis in Convex Geometry

Yangians and Classical Lie Algebras

Yangians and Classical Lie Algebras

Innovations and New Technologies (v.2)

Innovations and New Technologies (v.2)

Painlevé Transcendents

Painlevé Transcendents

The Interface Between Convex Geometry and Harmonic Analysis

The Interface Between Convex Geometry and Harmonic Analysis

Fourier Analysis in Convex Geometry

Fourier Analysis in Convex Geometry

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