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Author : H. Groemer
Publisher : Unknown
Page : 343 pages
File Size : 44,6 Mb
Release : 2014-05-22
Category : MATHEMATICS
ISBN : 110708881X
A full exposition of the classical theory of spherical harmonics and their use in proving stability results.
Author : Helmut Groemer
Publisher : Cambridge University Press
Page : 0 pages
File Size : 55,9 Mb
Release : 2009-09-17
Category : Mathematics
ISBN : 0521119650
This is the first comprehensive exposition of the application of spherical harmonics to prove geometric results. The author presents all the necessary tools from classical theory of spherical harmonics with full proofs. Groemer uses these tools to prove geometric inequalities, uniqueness results for projections and intersection by planes or half-spaces, stability results, and characterizations of convex bodies of a particular type, such as rotors in convex polytopes. Results arising from these analytical techniques have proved useful in many applications, particularly those related to stereology. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets.
Author : H. Groemer
Publisher : Cambridge University Press
Page : 343 pages
File Size : 43,5 Mb
Release : 1996-09-13
Category : Mathematics
ISBN : 9780521473187
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.
Author : William Elwood Byerly
Publisher : Unknown
Page : 306 pages
File Size : 54,9 Mb
Release : 1893
Category : Fourier series
ISBN : HARVARD:HS1FZZ
Author : Bozzano G Luisa
Publisher : Elsevier
Page : 769 pages
File Size : 49,6 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9780080934402
Handbook of Convex Geometry, Volume B offers a survey of convex geometry and its many ramifications and connections with other fields of mathematics, including convexity, lattices, crystallography, and convex functions. The selection first offers information on the geometry of numbers, lattice points, and packing and covering with convex sets. Discussions focus on packing in non-Euclidean spaces, problems in the Euclidean plane, general convex bodies, computational complexity of lattice point problem, centrally symmetric convex bodies, reduction theory, and lattices and the space of lattices. The text then examines finite packing and covering and tilings, including plane tilings, monohedral tilings, bin packing, and sausage problems. The manuscript takes a look at valuations and dissections, geometric crystallography, convexity and differential geometry, and convex functions. Topics include differentiability, inequalities, uniqueness theorems for convex hypersurfaces, mixed discriminants and mixed volumes, differential geometric characterization of convexity, reduction of quadratic forms, and finite groups of symmetry operations. The selection is a dependable source of data for mathematicians and researchers interested in convex geometry.
Author : Alexander Koldobsky
Publisher : American Mathematical Soc.
Page : 170 pages
File Size : 41,5 Mb
Release : 2014-11-12
Category : Electronic
ISBN : 9781470419523
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.
Author : Thomas Murray MacRobert
Publisher : Unknown
Page : 434 pages
File Size : 51,9 Mb
Release : 1948
Category : Harmonic functions
ISBN : UCSD:31822005660188
Author : Rolf Schneider
Publisher : Cambridge University Press
Page : 759 pages
File Size : 51,5 Mb
Release : 2014
Category : Mathematics
ISBN : 9781107601017
A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.
Author : Eric W. Weisstein
Publisher : CRC Press
Page : 3253 pages
File Size : 46,6 Mb
Release : 2002-12-12
Category : Mathematics
ISBN : 9781420035223
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 d
Author : Luca Brandolini,Leonardo Colzani,Alex Iosevich,Giancarlo Travaglini
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 44,9 Mb
Release : 2011-04-27
Category : Mathematics
ISBN : 9780817681722
Explores relationship between Fourier Analysis, convex geometry, and related areas; in the past, study of this relationship has led to important mathematical advances Presents new results and applications to diverse fields such as geometry, number theory, and analysis Contributors are leading experts in their respective fields Will be of interest to both pure and applied mathematicians
Author : Daniel A. Klain,Gian-Carlo Rota
Publisher : Cambridge University Press
Page : 196 pages
File Size : 47,5 Mb
Release : 1997-12-11
Category : Mathematics
ISBN : 0521596548
The purpose of this book is to present the three basic ideas of geometrical probability, also known as integral geometry, in their natural framework. In this way, the relationship between the subject and enumerative combinatorics is more transparent, and the analogies can be more productively understood. The first of the three ideas is invariant measures on polyconvex sets. The authors then prove the fundamental lemma of integral geometry, namely the kinematic formula. Finally the analogues between invariant measures and finite partially ordered sets are investigated, yielding insights into Hecke algebras, Schubert varieties and the quantum world, as viewed by mathematicians. Geometers and combinatorialists will find this a most stimulating and fruitful story.
Author : Ely M. Gelbard
Publisher : Unknown
Page : 18 pages
File Size : 47,5 Mb
Release : 1962
Category : Convex geometry
ISBN : UOM:39015095067172
Author : Dmitriy Bilyk,Laura De Carli,Alexander Petukhov,Alexander M. Stokolos,Brett D. Wick
Publisher : Springer Science & Business Media
Page : 400 pages
File Size : 50,7 Mb
Release : 2012-10-16
Category : Mathematics
ISBN : 9781461445654
Recent Advances in Harmonic Analysis and Applications features selected contributions from the AMS conference which took place at Georgia Southern University, Statesboro in 2011 in honor of Professor Konstantin Oskolkov's 65th birthday. The contributions are based on two special sessions, namely "Harmonic Analysis and Applications" and "Sparse Data Representations and Applications." Topics covered range from Banach space geometry to classical harmonic analysis and partial differential equations. Survey and expository articles by leading experts in their corresponding fields are included, and the volume also features selected high quality papers exploring new results and trends in Muckenhoupt-Sawyer theory, orthogonal polynomials, trigonometric series, approximation theory, Bellman functions and applications in differential equations. Graduate students and researchers in analysis will be particularly interested in the articles which emphasize remarkable connections between analysis and analytic number theory. The readers will learn about recent mathematical developments and directions for future work in the unexpected and surprising interaction between abstract problems in additive number theory and experimentally discovered optical phenomena in physics. This book will be useful for number theorists, harmonic analysts, algorithmists in multi-dimensional signal processing and experts in physics and partial differential equations.
Author : Richard J. Gardner
Publisher : Cambridge University Press
Page : 448 pages
File Size : 54,6 Mb
Release : 1995-09-29
Category : Art
ISBN : 0521451264
Develops the new field of retrieving information about geometric objects from projections on planes.
Author : Valeriy Volchkov
Publisher : Taylor & Francis US
Page : 476 pages
File Size : 50,8 Mb
Release : 2003-10-31
Category : Mathematics
ISBN : 140201628X
This book highlights new, previously unpublished results obtained in the last years in integral geometry and theory of convolution equations on bounded domains. All results included here are definitive and include for example the definitive version of the two-radii theorem, the solution of the support problem for ball mean values, the extreme variants of the Pompeiu problem, the definitive versions of uniqueness theorems for multiple trigonometric series with gaps. In order to make this book as self-contained as possible, we have gathered all prerequisites needed in the first part. In addition, each part of the book ends with comments in which not only other investigations are documented but also open problems dealing with a broader perspective are posed. A great number of applications to various branches of mathematics are also considered, for example, applications to the theory of approximations, discrete geometry, harmonic analysis, measure-preserving transformations, harmonic functions. Some of the material in this book has been the subject of lectures delivered by the author for advanced students, doctors and professors of mathematical faculty in various universities and so this book should be of interest to the graduate students and researchers in this area.