Decay of the fourier transform: Analytic and geometric aspects

Alex Iosevich; Elijah Liflyand

doi:10.1007/978-3-0348-0625-1_1

Decay of the fourier transform: Analytic and geometric aspects

Alex Iosevich
, Elijah Liflyand

Department of Mathematics

University of Rochester

Research output: Book/Report › Book › peer-review

46 Scopus citations

Abstract

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.

Original language	English
Publisher	Springer Basel
Number of pages	222
Volume	9783034806251
ISBN (Electronic)	9783034806251
ISBN (Print)	3034806248, 9783034806244
DOIs	https://doi.org/10.1007/978-3-0348-0625-1_1
State	Published - 1 Aug 2014

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Publisher Copyright:
© 2014 Springer Basel. Springer Basel.

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10.1007/978-3-0348-0625-1_1

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Decay of the fourier transform: Analytic and geometric aspects

Abstract

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