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Fourier Analysis and Convexity (Applied and Numerical Harmonic Analysis)

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Synopses & Reviews

Publisher Comments:

Over the course of the last century, the systematic exploration of the relationship between Fourier analysis and other branches of mathematics has lead to important advances in geometry, number theory, and analysis, stimulated in part by Hurwitz's proof of the isoperimetric inequality using Fourier series.                                                             This unified, self-contained volume is dedicated to Fourier analysis, convex geometry, and related topics. Specific topics covered include: * the geometric properties of convex bodies * the study of Radon transforms * the geometry of numbers * the study of translational tilings using Fourier analysis * irregularities in distributions * Lattice point problems examined in the context of number theory, probability theory, and Fourier analysis * restriction problems for the Fourier transform   The book presents both a broad overview of Fourier analysis and convexity as well as an intricate look at applications in some specific settings; it will be useful to graduate students and researchers in harmonic analysis, convex geometry, functional analysis, number theory, computer science, and combinatorial analysis. A wide audience will benefit from the careful demonstration of how Fourier analysis is used to distill the essence of many mathematical problems in a natural and elegant way. Contributors: J. Beck, C. Berenstein, W.W.L. Chen, B. Green, H. Groemer, A. Koldobsky, M. Kolountzakis, A. Magyar, A.N. Podkorytov, B. Rubin, D. Ryabogin, T. Tao, G. Travaglini, A. Zvavitch

Synopsis:

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

Table of Contents

Preface Contributors Lattice Point Problems: Crossroads of Number Theory, Probability Theory, and Fourier Analysis Totally Geodesic Radon Transform of L^P-Functions on Real Hyperbolic Space Fourier Techniques in the Theory of Irregularities of Point Distributions Spectral Structure of Sets of Integers One-Hundred Years of Fourier Series and Spherical Harmonics in Convexity Fourier Analytic Methods in the Study of Projections and Sections of Convex Bodies The Study of Translational Tiling with Fourier Analysis Discrete Maximal Functions and Ergodic Theorems Related to Polynomials What is it Possible to Say About an Asymptotic of the Fourier Transform of the Characteristic Function of a Two-Dimensional Convex Body with Nonsmooth Boundary? Some Recent Progress on the Restriction Conjecture Average Decay of the Fourier Transform Index

Product Details

ISBN:
9780817632632
Editor:
Brandolini, Luca
Editor:
Colzani, Leonardo
Other:
Brandolini, Luca
Editor:
Brandolini, Luca
Editor:
Colzani, Leonardo
Editor:
Iosevich, Alex
Author:
Iosevich, Alex
Author:
Brandolini, Luca
Author:
Travaglini, Giancarlo
Author:
Colzani, Leonardo
Editor:
Iosevich, Alex
Publisher:
Birkhauser
Subject:
Mathematical Analysis
Subject:
Geometry - General
Subject:
Infinity
Subject:
Geometry, analytic
Subject:
Fourier analysis
Subject:
abstract harmonic analysis
Subject:
Convex and Discrete Geometry
Subject:
Number Theory
Subject:
Functional Analysis
Subject:
Mathematics - General
Edition Number:
1
Edition Description:
Book
Series:
Applied and Numerical Harmonic Analysis
Publication Date:
20040831
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
277
Dimensions:
235 x 155 mm 520 gr

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Fourier Analysis and Convexity (Applied and Numerical Harmonic Analysis) New Hardcover
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Product details 277 pages Birkhauser Boston - English 9780817632632 Reviews:
"Synopsis" by , 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
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