Geometric Applications Of Fourier Series And Spherical Harmonics

Author : H. Groemer
Publisher :
ISBN 13 : 9781107088818
Total Pages : 343 pages
Book Rating : 4.1X/5 ( download)

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Download or read book Geometric Applications of Fourier Series and Spherical Harmonics written by H. Groemer and published by . This book was released on 2014-05-22 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: A full exposition of the classical theory of spherical harmonics and their use in proving stability results.

Author : Helmut Groemer
Publisher : Cambridge University Press
ISBN 13 : 9780521119658
Total Pages : 0 pages
Book Rating : 4.50/5 ( download)

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Download or read book Geometric Applications of Fourier Series and Spherical Harmonics written by Helmut Groemer and published by Cambridge University Press. This book was released on 2009-09-17 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 0521473187
Total Pages : 343 pages
Book Rating : 4.87/5 ( download)

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Download or read book Geometric Applications of Fourier Series and Spherical Harmonics written by H. Groemer and published by Cambridge University Press. This book was released on 1996-09-13 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :
ISBN 13 :
Total Pages : 312 pages
Book Rating : 4.EK/5 ( download)

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Download or read book An Elementary Treatise on Fourier's Series and Spherical, Cylindrical, and Ellipsoidal Harmonics written by William Elwood Byerly and published by . This book was released on 1893 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Alexander Koldobsky
Publisher : American Mathematical Soc.
ISBN 13 : 1470419521
Total Pages : 178 pages
Book Rating : 4.23/5 ( download)

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Download or read book Fourier Analysis in Convex Geometry written by Alexander Koldobsky and published by American Mathematical Soc.. This book was released on 2014-11-12 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Bozzano G Luisa
Publisher : Elsevier
ISBN 13 : 0080934404
Total Pages : 769 pages
Book Rating : 4.02/5 ( download)

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Download or read book Handbook of Convex Geometry written by Bozzano G Luisa and published by Elsevier. This book was released on 2014-06-28 with total page 769 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Rolf Schneider
Publisher : Cambridge University Press
ISBN 13 : 1107601010
Total Pages : 759 pages
Book Rating : 4.17/5 ( download)

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Download or read book Convex Bodies: The Brunn–Minkowski Theory written by Rolf Schneider and published by Cambridge University Press. This book was released on 2014 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 1420035223
Total Pages : 3253 pages
Book Rating : 4.23/5 ( download)

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Download or read book CRC Concise Encyclopedia of Mathematics written by Eric W. Weisstein and published by CRC Press. This book was released on 2002-12-12 with total page 3253 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Springer Science & Business Media
ISBN 13 : 0817681728
Total Pages : 268 pages
Book Rating : 4.22/5 ( download)

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Download or read book Fourier Analysis and Convexity written by Luca Brandolini and published by Springer Science & Business Media. This book was released on 2011-04-27 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Thomas Murray MacRobert
Publisher :
ISBN 13 :
Total Pages : 396 pages
Book Rating : 4.32/5 ( download)

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Download or read book Spherical Harmonics written by Thomas Murray MacRobert and published by . This book was released on 1948 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: