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E-BOOK
Title Decay of the Fourier transform : analytic and geometric aspects / Alex Losevich ; Elijah Liflyand.
Imprint Basel [Switzerland] : Springer, 2014.
©2014

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Description 1 online resource (226 pages)
Bibliog. Includes bibliographical references and index.
Note Available only to authorized UTEP users.
Print version record.
Subject Fourier analysis -- Data processing.
Geometric analysis -- Data processing.
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.
Summary The Plancherel formula says that the L2 norm of the function is equal to the L2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L2 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 L2 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.
Other Author Liflyand, Elijah, author.
Other Title Print version: Losevich, Alex. Decay of the Fourier transform : analytic and geometric aspects. Basel, [Switzerland] : Springer, ©2014 xii, 222 pages 9783034806244