Decay of the Fourier Transform

Analytic and Geometric Aspects

  • Alex Iosevich
  • Elijah Liflyand

Table of contents

  1. Front Matter
    Pages i-xii
  2. Preliminaries

    1. Front Matter
      Pages 1-1
    2. Alex Iosevich, Elijah Liflyand
      Pages 3-10
    3. Alex Iosevich, Elijah Liflyand
      Pages 11-16
  3. Analytic (and Geometric) Aspects

    1. Front Matter
      Pages 17-17
    2. Alex Iosevich, Elijah Liflyand
      Pages 19-46
    3. Alex Iosevich, Elijah Liflyand
      Pages 47-91
    4. Alex Iosevich, Elijah Liflyand
      Pages 93-126
  4. Geometric (and Analytic) Aspects

  5. Back Matter
    Pages 205-222

About this book

Introduction

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.

Keywords

Fourier transform bounded variation curvature decay rate spherical average

Authors and affiliations

  • Alex Iosevich
    • 1
  • Elijah Liflyand
    • 2
  1. 1.Department of MathematicsUniversity of RochesterRochesterUSA
  2. 2.Department of MathematicsBar-Ilan UniversityRamat-GanIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0625-1
  • Copyright Information Springer Basel 2014
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0624-4
  • Online ISBN 978-3-0348-0625-1
  • About this book