Decay of the Fourier Transform
Analytic and Geometric Aspects
Authors: Iosevich, Alex, Liflyand, Elijah
Free Preview Only book where the decay rate of the Fourier transform is the dominant theme
 Systematic examination of the concepts
 Focus on interaction between the analytic and geometric approaches of Fourier theory
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 About this book

The Plancherel formula says that the L^2 norm of the function is equal to the L^2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L^2 function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L^2 setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.
 Reviews

“The overall presentation is clear and the reader is carefully guided through this territory which is marked by a beautiful blend of ideas and techniques from analysis, geometry and also number theory.” (Wien R. Steinbauer, Monatshefte für Mathematik, Vol. 185, 2018)
“It is an introduction to current topics in Fourier analysis, to be read and appreciated by mathematicians … . the book is carefully designed and well written. It does a very good job of familiarizing the reader with the relevant techniques and results, relying on a beautiful interplay of analysis, geometry and number theory.” (Hartmut Führ, Mathematical Reviews, January, 2016)
 Table of contents (9 chapters)


Introduction
Pages 310

Basic Properties of the Fourier Transform
Pages 1116

Oscillatory Integrals
Pages 1946

The Fourier Transform of Convex and Oscillating Functions
Pages 4791

The Fourier Transform of a Radial Function
Pages 93126

Table of contents (9 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Decay of the Fourier Transform
 Book Subtitle
 Analytic and Geometric Aspects
 Authors

 Alex Iosevich
 Elijah Liflyand
 Copyright
 2014
 Publisher
 Birkhäuser Basel
 Copyright Holder
 Springer Basel
 eBook ISBN
 9783034806251
 DOI
 10.1007/9783034806251
 Hardcover ISBN
 9783034806244
 Edition Number
 1
 Number of Pages
 XII, 222
 Number of Illustrations
 3 b/w illustrations, 2 illustrations in colour
 Topics