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Functions of Bounded Variation and Their Fourier Transforms

  • Elijah Liflyand

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. One-dimensional Case

    1. Front Matter
      Pages 9-10
    2. Elijah Liflyand
      Pages 11-55
    3. Elijah Liflyand
      Pages 57-83
    4. Elijah Liflyand
      Pages 85-98
    5. Elijah Liflyand
      Pages 99-114
  3. Multi-dimensional Case

    1. Front Matter
      Pages 115-116
    2. Elijah Liflyand
      Pages 117-131
    3. Elijah Liflyand
      Pages 133-141
    4. Elijah Liflyand
      Pages 143-160
    5. Elijah Liflyand
      Pages 161-177
    6. Elijah Liflyand
      Pages 179-187
  4. Back Matter
    Pages 189-218

About this book

Introduction

Functions of bounded variation represent an important class of functions. Studying their Fourier transforms is a valuable means of revealing their analytic properties. Moreover, it brings to light new interrelations between these functions and the real Hardy space and, correspondingly, between the Fourier transform and the Hilbert transform.  

This book is divided into two major parts, the first of which addresses several aspects of the behavior of the Fourier transform of a function of bounded variation in dimension one. In turn, the second part examines the Fourier transforms of multivariate functions with bounded Hardy variation. The results obtained are subsequently applicable to problems in approximation theory, summability of the Fourier series and integrability of trigonometric series.   

Keywords

bounded variation cosine and sine fourier transforms hardy space hilbert transform integrability asymptotic behavior hardy variation

Authors and affiliations

  • Elijah Liflyand
    • 1
  1. 1.Department of MathematicsBar-Ilan UniversityRamat-GanIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-04429-9
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-04428-2
  • Online ISBN 978-3-030-04429-9
  • Series Print ISSN 2296-5009
  • Series Online ISSN 2296-5017
  • Buy this book on publisher's site