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Geometric Applications of Fourier Series and Spherical Harmonics

Geometric Applications of Fourier Series and Spherical Harmonics
Author: H. Groemer
Publisher: Cambridge University Press
Total Pages: 343
Release: 1996-09-13
Genre: Mathematics
ISBN: 0521473187

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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.


An Elementary Treatise on Fourier's Series and Spherical, Cylindric, and Ellipsoidal Harmonics

An Elementary Treatise on Fourier's Series and Spherical, Cylindric, and Ellipsoidal Harmonics
Author: William Elwood Byerly
Publisher: Cosimo, Inc.
Total Pages: 301
Release: 2007-01-01
Genre: Science
ISBN: 1602063052

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First published in 1893, Byerly's classic treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonics has been used in classrooms for well over a century. This practical exposition acts as a primer for fields such as wave mechanics, advanced engineering, and mathematical physics. Topics covered include: . development in trigonometric series . convergence on Fourier's series . solution of problems in physics by the aid of Fourier's integrals and Fourier's series . zonal harmonics . spherical harmonics . cylindrical harmonics (Bessel's functions) . and more. Containing 190 exercises and a helpful appendix, this reissue of Fourier's Series will be welcomed by students of higher mathematics everywhere. American mathematician WILLIAM ELWOOD BYERLY (1849-1935) also wrote Elements of Differential Calculus (1879) and Elements of Integral Calculus (1881).


Fourier Analysis in Convex Geometry

Fourier Analysis in Convex Geometry
Author: Alexander Koldobsky
Publisher: American Mathematical Soc.
Total Pages: 178
Release: 2014-11-12
Genre: Mathematics
ISBN: 1470419521

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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.


Integral Geometry and Convolution Equations

Integral Geometry and Convolution Equations
Author: Valeriy Volchkov
Publisher: Taylor & Francis US
Total Pages: 476
Release: 2003-10-31
Genre: Mathematics
ISBN: 9781402016288

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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.


An Elementary Treatise on Fourier's Series and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics, Pp. 1-283

An Elementary Treatise on Fourier's Series and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics, Pp. 1-283
Author: William Elwood Byerly
Publisher: Trieste Publishing
Total Pages: 298
Release: 2017-09-17
Genre: History
ISBN: 9780649053841

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Trieste Publishing has a massive catalogue of classic book titles. Our aim is to provide readers with the highest quality reproductions of fiction and non-fiction literature that has stood the test of time. The many thousands of books in our collection have been sourced from libraries and private collections around the world.The titles that Trieste Publishing has chosen to be part of the collection have been scanned to simulate the original. Our readers see the books the same way that their first readers did decades or a hundred or more years ago. Books from that period are often spoiled by imperfections that did not exist in the original. Imperfections could be in the form of blurred text, photographs, or missing pages. It is highly unlikely that this would occur with one of our books. Our extensive quality control ensures that the readers of Trieste Publishing's books will be delighted with their purchase. Our staff has thoroughly reviewed every page of all the books in the collection, repairing, or if necessary, rejecting titles that are not of the highest quality. This process ensures that the reader of one of Trieste Publishing's titles receives a volume that faithfully reproduces the original, and to the maximum degree possible, gives them the experience of owning the original work.We pride ourselves on not only creating a pathway to an extensive reservoir of books of the finest quality, but also providing value to every one of our readers. Generally, Trieste books are purchased singly - on demand, however they may also be purchased in bulk. Readers interested in bulk purchases are invited to contact us directly to enquire about our tailored bulk rates.


Geometric Tomography

Geometric Tomography
Author: Richard J. Gardner
Publisher: Cambridge University Press
Total Pages: 448
Release: 1995-09-29
Genre: Art
ISBN: 9780521451260

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Develops the new field of retrieving information about geometric objects from projections on planes.


Fourier Analysis and Convexity

Fourier Analysis and Convexity
Author: Luca Brandolini
Publisher: Springer Science & Business Media
Total Pages: 268
Release: 2011-04-27
Genre: Mathematics
ISBN: 0817681728

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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


Convex Bodies

Convex Bodies
Author: Rolf Schneider
Publisher: Cambridge University Press
Total Pages: 506
Release: 1993-02-25
Genre: Mathematics
ISBN: 0521352207

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A comprehensive introduction to convex bodies giving full proofs for some deeper theorems which have never previously been brought together.