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Decay of the Fourier Transform

Analytic and Geometric Aspects

Authors: Iosevich, Alex, Liflyand, Elijah

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  • 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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  • ISBN 978-3-0348-0625-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
Hardcover n/a
  • ISBN 978-3-0348-0624-4
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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)

Table of contents (9 chapters)

Buy this book

eBook n/a
  • ISBN 978-3-0348-0625-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
Hardcover n/a
  • ISBN 978-3-0348-0624-4
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Decay of the Fourier Transform
Book Subtitle
Analytic and Geometric Aspects
Authors
Copyright
2014
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0625-1
DOI
10.1007/978-3-0348-0625-1
Hardcover ISBN
978-3-0348-0624-4
Edition Number
1
Number of Pages
XII, 222
Number of Illustrations
3 b/w illustrations, 2 illustrations in colour
Topics