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Fourier Analysis and Approximation

One Dimensional Theory

  • Book
  • © 1971


Part of the book series: Lehrbücher und Monographien aus dem Gebiete der exakten Wissenschaften (LMW, volume 1)

Part of the book sub series: Mathematische Reihe (LMW/MA)

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About this book

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.

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Table of contents (14 chapters)

  1. Preliminaries

  2. Approximation by Singular Integrals

  3. Fourier Transforms

  4. Hilbert Transforms

  5. Characterization of Certain Function Classes

  6. Saturation Theory

Authors and Affiliations

  • Rheinisch Westfälische Technische Hochschule, Aachen, Germany

    Paul L. Butzer, Rolf J. Nessel

Bibliographic Information

  • Book Title: Fourier Analysis and Approximation

  • Book Subtitle: One Dimensional Theory

  • Authors: Paul L. Butzer, Rolf J. Nessel

  • Series Title: Lehrbücher und Monographien aus dem Gebiete der exakten Wissenschaften

  • DOI:

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag Basel 1971

  • Softcover ISBN: 978-3-0348-7450-2Published: 03 May 2012

  • eBook ISBN: 978-3-0348-7448-9Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XVI, 553

  • Topics: Analysis

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