geometric applications of fourier series and spherical harmonics encyclopedia of mathematics and its applications

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Geometric Applications Of Fourier Series And Spherical Harmonics

Author : H. Groemer
ISBN : 0521473187
Genre : Mathematics
File Size : 71. 25 MB
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This book provides a comprehensive presentation of geometric results, primarily from the theory of convex sets, that have been proved by the use of Fourier series or spherical harmonics. An important feature of the book is that all necessary tools from the classical theory of spherical harmonics are presented with full proofs. These tools are used to prove geometric inequalities, stability results, uniqueness results for projections and intersections by hyperplanes or half-spaces and characterisations of rotors in convex polytopes. Again, full proofs are given. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets. This treatise will be welcomed both as an introduction to the subject and as a reference book for pure and applied mathematics.

Proceedings Of The International Conference Integral Geometry And Convexity

Author : Eric Grinberg
ISBN : 9789812565136
Genre : Science
File Size : 31. 93 MB
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Integral geometry, known as geometric probability in the past, originated from Buffon's needle experiment. Remarkable advances have been made in several areas that involve the theory of convex bodies. This volume brings together contributions by leading international researchers in integral geometry, convex geometry, complex geometry, probability, statistics, and other convexity related branches. The articles cover both recent results and exciting directions for future research.

Integral Geometry And Convexity

Author :
ISBN : 9789814479271
Genre :
File Size : 26. 7 MB
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Asymptotic Geometric Analysis Part I

Author : Shiri Artstein-Avidan
ISBN : 9781470421939
Genre : Functional analysis
File Size : 23. 5 MB
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The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomenon", one of the most powerful tools of the theory, responsible for many counterintuitive results. A central theme in this book is the interaction of randomness and pattern. At first glance, life in high dimension seems to mean the existence of multiple "possibilities", so one may expect an increase in the diversity and complexity as dimension increases. However, the concentration of measure and effects caused by convexity show that this diversity is compensated and order and patterns are created for arbitrary convex bodies in the mixture caused by high dimensionality. The book is intended for graduate students and researchers who want to learn about this exciting subject. Among the topics covered in the book are convexity, concentration phenomena, covering numbers, Dvoretzky-type theorems, volume distribution in convex bodies, and more.

Crc Concise Encyclopedia Of Mathematics Second Edition

Author : Eric W. Weisstein
ISBN : 9781420035223
Genre : Mathematics
File Size : 83. 87 MB
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Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the dedication of author Eric Weisstein to collecting, cataloging, and referencing mathematical facts, formulas, and definitions. He has now updated most of the original entries and expanded the Encyclopedia to include 1000 additional pages of illustrated entries. The accessibility of the Encyclopedia along with its broad coverage and economical price make it attractive to the widest possible range of readers and certainly a must for libraries, from the secondary to the professional and research levels. For mathematical definitions, formulas, figures, tabulations, and references, this is simply the most impressive compendium available.

Mathematical Reviews

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ISBN : UOM:39015056640611
Genre : Mathematics
File Size : 89. 90 MB
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Bpr

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ISBN : STANFORD:36105117254628
Genre : American literature
File Size : 40. 77 MB
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Introduction To Radon Transforms

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ISBN : 9780521854597
Genre :
File Size : 26. 11 MB
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American Journal Of Mathematics

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ISBN : UCAL:B5127979
Genre :
File Size : 72. 29 MB
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Spherical Harmonics In P Dimensions

Author : Costas Efthimiou
ISBN : 9789814596718
Genre : Mathematics
File Size : 81. 22 MB
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The current book makes several useful topics from the theory of special functions, in particular the theory of spherical harmonics and Legendre polynomials in arbitrary dimensions, available to undergraduates studying physics or mathematics. With this audience in mind, nearly all details of the calculations and proofs are written out, and extensive background material is covered before exploring the main subject matter. Contents:Introduction and MotivationWorking in p DimensionsOrthogonal PolynomialsSpherical Harmonics in p DimensionsSolutions to Problems Readership: Undergraduate and graduate students in mathematical physics and differential equations. Key Features:Accessible to everyone (including undergraduate students who have some knowledge in mathematics)Presents a topic that, although well-studied, is not widely disseminated in booksSolutions to all end-of-chapter problems with all the necessary details are given in the final chapter of the bookKeywords:Spherical Harmonics;Special Functions;Mathematical Physics;Green's Functions;Legendre Polynomials

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