Decay of the Fourier Transform: Analytic and Geometric Aspects by Alex IosevichDecay of the Fourier Transform: Analytic and Geometric Aspects by Alex Iosevich

Decay of the Fourier Transform: Analytic and Geometric Aspects

byAlex Iosevich, Elijah Liflyand

Hardcover | October 10, 2014

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The Plancherel formula says that theL^2 norm of the function is equal to theL^2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of anL^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 originalL^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.
Title:Decay of the Fourier Transform: Analytic and Geometric AspectsFormat:HardcoverDimensions:222 pagesPublished:October 10, 2014Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034806248

ISBN - 13:9783034806244


Table of Contents

Foreword.- Introduction.- Chapter 1. Basic properties of the Fourier transform.- Chapter 2. Oscillatory integrals and Fourier transforms in one variable.- Chapter 3. The Fourier transform of an oscillating function.- Chapter 4. The Fourier transform of a radial function.- Chapter 5. Multivariate extensions.- Appendix.- Bibliography.

Editorial Reviews

"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)