Decay of the Fourier Transform
Analytic and Geometric Aspects| By: | Alex Iosevich; Elijah Liflyand |
| Publisher: | Springer Nature |
| Print ISBN: | 9783034806244 |
| eText ISBN: | 9783034806251 |
| Edition: | 0 |
| Copyright: | 2014 |
| Format: | Page Fidelity |
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Table of Contents
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.