Decay of the Fourier Transform

Analytic and Geometric Aspects

Authors: Iosevich, Alex, Liflyand, Elijah

  • 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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eBook $79.99
price for USA (gross)
  • ISBN 978-3-0348-0625-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-0348-0624-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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

“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)

  • Introduction

    Iosevich, Alex (et al.)

    Pages 3-10

  • Basic Properties of the Fourier Transform

    Iosevich, Alex (et al.)

    Pages 11-16

  • Oscillatory Integrals

    Iosevich, Alex (et al.)

    Pages 19-46

  • The Fourier Transform of Convex and Oscillating Functions

    Iosevich, Alex (et al.)

    Pages 47-91

  • The Fourier Transform of a Radial Function

    Iosevich, Alex (et al.)

    Pages 93-126

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-0348-0625-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-0348-0624-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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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 and Tables
3 b/w illustrations, 2 illustrations in colour
Topics