Skip to main content
  • Book
  • © 2019

Functions of Bounded Variation and Their Fourier Transforms

Birkhäuser

Authors:

  • Covers almost all the aspects of the behavior of the Fourier transforms of functions of bounded variation
  • Many known and new spaces are considered
  • A must to read for those who are interested in function spaces and their interrelations

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

Buy it now

Buying options

eBook USD 44.99 USD 89.00
49% discount Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 59.99 USD 119.99
50% discount Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, log in via an institution to check for access.

Table of contents (9 chapters)

  1. Front Matter

    Pages i-xxiv
  2. One-dimensional Case

    1. Front Matter

      Pages 9-10
    2. A toolkit

      • Elijah Liflyand
      Pages 11-55
    3. Functions with derivative in a Hardy space

      • Elijah Liflyand
      Pages 57-83
    4. Integrability spaces: wide, wider and widest

      • Elijah Liflyand
      Pages 85-98
    5. Sharper results

      • Elijah Liflyand
      Pages 99-114
  3. Multi-dimensional Case

    1. Front Matter

      Pages 115-116
    2. A toolkit for several dimensions

      • Elijah Liflyand
      Pages 117-131
    3. Integrability of the Fourier transforms

      • Elijah Liflyand
      Pages 133-141
    4. Sharp results

      • Elijah Liflyand
      Pages 143-160
    5. Bounded variation and sampling

      • Elijah Liflyand
      Pages 161-177
    6. Multidimensional case: radial functions

      • Elijah Liflyand
      Pages 179-187
  4. Back Matter

    Pages 189-218

About this book

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.   


Authors and Affiliations

  • Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel

    Elijah Liflyand

Bibliographic Information

Buy it now

Buying options

eBook USD 44.99 USD 89.00
49% discount Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 59.99 USD 119.99
50% discount Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access