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Birkhäuser

Convergence and Summability of Fourier Transforms and Hardy Spaces

  • Book
  • © 2017

Overview

Authors:
  1. Ferenc Weisz

    1. Department of Numerical Analysis, Eötvös Loránd University, Budapest, Hungary

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  • Explores comprehensively the summability of Fourier transforms as well as the theory of Hardy spaces
  • Gathers classical results as well as recent results from the past 20-30 years
  • Considers strong summability introduced by current methodology

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

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xxii
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  2. One-Dimensional Hardy Spaces and Fourier Transforms

    1. Front Matter

      Pages 1-1
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    2. One-Dimensional Hardy Spaces

      • Ferenc Weisz
      Pages 3-70

    3. One-Dimensional Fourier Transforms

      • Ferenc Weisz
      Pages 71-133

  3. Multi-Dimensional Hardy Spaces and Fourier Transforms

    1. Front Matter

      Pages 135-135
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    2. Multi-Dimensional Hardy Spaces

      • Ferenc Weisz
      Pages 137-202

    3. Multi-Dimensional Fourier Transforms

      • Ferenc Weisz
      Pages 203-227

    4. ℓ q -Summability of Multi-Dimensional Fourier Transforms

      • Ferenc Weisz
      Pages 229-382

    5. Rectangular Summability of Multi-Dimensional Fourier Transforms

      • Ferenc Weisz
      Pages 383-411

  4. Back Matter

    Pages 413-435
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Keywords

About this book

This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces. To do so, it studies a general summability method known as theta-summation, which encompasses all the well-known summability methods, such as the Fejér, Riesz, Weierstrass, Abel, Picard, Bessel and Rogosinski summations. 
Following on the classic books by Bary (1964) and Zygmund (1968), this is the first book that considers strong summability introduced by current methodology. A further unique aspect is that the Lebesgue points are also studied in the theory of multi-dimensional summability. In addition to classical results, results from the past 20-30 years – normally only found in scattered research papers – are also gathered and discussed, offering readers a convenient “one-stop” source to support their work. As such, the book will be useful for researchers, graduate and postgraduate students alike.

Authors and Affiliations

  • Department of Numerical Analysis, Eötvös Loránd University, Budapest, Hungary

    Ferenc Weisz

About the author

Ferenc Weisz is Professor at the Department of Numerical Analysis of the Eötvös Loránd University in Budapest, Hungary.

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