Semen Grigor evich Gindikin's Books

The Method of Newton’s Polyhedron in the Theory of Partial Differential Equations

By: Semen G. Gindikin,L. Volevich

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The Method of Newton’s Polyhedron in the Theory of Partial Differential Equations

By: Semen G. Gindikin,L. Volevich

One service mathematics has rendered the 'Et moi, .. ., si j'avait su comment cn rcvenir, human race. It has put common sense back. je n'y serais point aile.' where it bdongs, on the topmost shelf neAt Jules Verne to the dusty canister labelled 'discarded non- sense'. The series is divergent; therefore we may be Eric T. Bdl able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com- puter science ..: 'One service category theory has rendered mathematics .. .'. All a, rguably true. And all statements obtainable this way form part of the raison d'etre of this series.

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Page Count

286

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0792320379

ISBN 13

9780792320371

Algebraic Logic

By: Semen Grigorʹevich Gindikin

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Algebraic Logic

By: Semen Grigorʹevich Gindikin

The popular literature on mathematical logic is rather extensive and written for the most varied categories of readers. College students or adults who read it in their free time may find here a vast number of thought-provoking logical problems. The reader who wishes to enrich his mathematical background in the hope that this will help him in his everyday life can discover detailed descriptions of practical (and quite often -- not so practical!) applications of logic. The large number of popular books on logic has given rise to the hope that by applying mathematical logic, students will finally learn how to distinguish between necessary and sufficient conditions and other points of logic in the college course in mathematics. But the habit of teachers of mathematical analysis, for example, to stick to problems dealing with sequences without limit, uniformly continuous functions, etc. has, unfortunately, led to the writing of textbooks that present prescriptions for the mechanical construction of definitions of negative concepts which seem to obviate the need for any thinking on the reader's part. We are most certainly not able to enumerate everything the reader may draw out of existing books on mathematical logic, however.

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Page Count

386

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387961798

ISBN 13

9780387961798

Selected Topics in Integral Geometry

By: Izrailʹ Moiseevich Gelʹfand,Semen Grigorʹevich Gindikin,Mark Iosifovich Graev

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Selected Topics in Integral Geometry

By: Izrailʹ Moiseevich Gelʹfand,Semen Grigorʹevich Gindikin,Mark Iosifovich Graev

The miracle of integral geometry is that it is often possible to recover a function on a manifold just from the knowledge of its integrals over certain submanifolds. The founding example is the Radon transform, introduced at the beginning of the 20th century. Since then, many other transforms were found, and the general theory was developed. Moreover, many important practical applications were discovered. The best known, but by no means the only one, being to medical tomography. This book is a general introduction to integral geometry, the first from this point of view for almost four decades. The authors, all leading experts in the field, represent one of the most influential schools in integral geometry. The book presents in detail basic examples of integral geometry problems, such as the Radon transform on the plane and in space, the John transform, the Minkowski-Funk transform, integral geometry on the hyperbolic plane and in the hyperbolic space, the horospherical transform and its relation to representations of $SL(2,\mathbb C)$, integral geometry on quadrics, etc. The study of these examples allows the authors to explain important general topics of integral geometry, such as the Cavalieri conditions, local and nonlocal inversion formulas, and overdetermined problems in integral geometry. Many of the results in the book were obtained by the authors in the course of their career-long work in integral geometry. This book is suitable for graduate students and researchers working in integral geometry and its applications.

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Page Count

136

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821829327

ISBN 13

9780821829325

Selected Topics in Integral Geometry

By: Izrail_ Moiseevich Gel_fand,Semen Grigor_evich Gindikin,Mark Iosifovich Graev

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Selected Topics in Integral Geometry

By: Izrail_ Moiseevich Gel_fand,Semen Grigor_evich Gindikin,Mark Iosifovich Graev

The miracle of integral geometry is that it is often possible to recover a function on a manifold just from the knowledge of its integrals over certain submanifolds. The founding example is the Radon transform, introduced at the beginning of the 20th century. Since then, many other transforms were found, and the general theory was developed. Moreover, many important practical applications were discovered, the best known, but by no means the only one, being to medical tomography. The present book is a general introduction to integral geometry, the first from this point of view for almost four decades. The authors, all leading experts in the field, represent one of the most influential schools in integral geometry. The book presents in detail basic examples of integral geometry problems, such as the Radon transform on the plane and in space, the John transform, the Minkowski-Funk transform, integral geometry on the hyperbolic plane and in the hyperbolic space, the horospherical transform and its relation to representations of $SL(2,\mathbb C)$, integral geometry on quadrics, etc. The study of these examples allows the authors to explain important general topics of integral geometry, such as the Cavalieri conditions, local and nonlocal inversion formulas, and overdetermined problems. Many of the results in the book were obtained by the authors in the course of their career-long work in integral geometry.

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Page Count

192

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821898043

ISBN 13

9780821898048

Distributions and Convolution Equations

By: Semen Grigorʹevich Gindikin,Leonid Romanovich Volevich

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Distributions and Convolution Equations

By: Semen Grigorʹevich Gindikin,Leonid Romanovich Volevich

The authors apply the results of many years of their own original research to a systematic presentation of the theory of distributions in this monograph which can also be used as a (very expensive) textbook on the theory of distribution for graduate students. The first part is devoted to the Cauchy problem, while the second part deals with the Wiener-Hopf equation and related topics in the theory of boundary value problems for convolution equations. To make their work more accessible to readers new to this field, the authors restrict initial treatment of problems to the half-line and formulate only principal results, in their simplest form. Special results and possible generalizations are presented as problems and exercises. Annotation copyrighted by Book News, Inc., Portland, OR

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Page Count

482

Publisher

CRC Press

Published Date

ISBN 10

2881247539

ISBN 13

9782881247538

Tube Domains and the Cauchy Problem

By: Semen Grigorʹevich Gindikin

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Tube Domains and the Cauchy Problem

By: Semen Grigorʹevich Gindikin

This book is dedicated to two problems. The first concerns the description of maximal exponential growth of functions or distributions for which the Cauchy problem is well posed. The descriptions presented in the language of the behaviour of the symbol in a complex domain. The second problem concerns the structure of and explicit formulas for differential operators with large automorphism groups. It is suitable as an advanced graduate text in courses in partial differential equations and the theory of distributions.

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Page Count

144

Publisher

American Mathematical Soc.

ISBN 10

0821897403

ISBN 13

9780821897409

Book's by Semen Grigor evich Gindikin

The Method of Newton’s Polyhedron in the Theory of Partial Differential Equations

The Method of Newton’s Polyhedron in the Theory of Partial Differential Equations

Algebraic Logic

Algebraic Logic

Selected Topics in Integral Geometry

Selected Topics in Integral Geometry

Selected Topics in Integral Geometry

Selected Topics in Integral Geometry

Distributions and Convolution Equations

Distributions and Convolution Equations

Tube Domains and the Cauchy Problem

Tube Domains and the Cauchy Problem

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