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Twentieth Century Harmonic Analysis

A Celebration

  • Book
  • © 2001

Overview

Editors:
  1. James S. Byrnes

    1. Prometheus Inc., Newport, USA
      University of Massachusetts at Boston, Boston, USA

    View editor publications

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Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry (NAII, volume 33)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xi
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  2. The Papers

    1. Front Matter

      Pages 1-1
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    2. On the Uncertainty Principle in Harmonic Analysis

      • V. P. Havin
      Pages 3-29

    3. Operator Theory and Harmonic Analysis

      • H. S. Shapiro
      Pages 31-56

    4. Probabilities and Baire’s theory in harmonic analysis

      • J.-P. Kahane
      Pages 57-72

    5. Representations of Gabor frame operators

      • A. J. E. M. Janssen
      Pages 73-101

    6. Does Order Matter

      • T. W. Körner
      Pages 103-125

    7. Wavelet expansions, function spaces and multifractal analysis

      • S. Jaffard
      Pages 127-144

    8. Some Plots of Bessel Functions of Two Variables

      • F. A. Grünbaum
      Pages 145-149

    9. Lesser Known FFT Algorithms

      • R. Tolimieri, M. An
      Pages 151-162

    10. The Phase Problem of X-ray Crystallography

      • H. A. Hauptman
      Pages 163-171

    11. Multiwindow Gabor-type Representations and Signal Representation by Partial Information

      • Y. Y. Zeevi
      Pages 173-199

    12. Some polynomial extremal problems which emerged in the twentieth century

      • Bahman Saffari
      Pages 201-233

    13. The Problem of Efficient Inversions and Bezout Equations

      • Nikolai Nikolski
      Pages 235-269

    14. Harmonic Analysis as found in Analytic Number Theory

      • Hugh L. Montgomery
      Pages 271-293

    15. Mathematics of Radar

      • Bill Moran
      Pages 295-328

    16. The Mathematical Theory of Wavelets

      • G. Weiss, E. N. Wilson
      Pages 329-366

  3. Problems

    1. Front Matter

      Pages 367-367
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    2. Assorted Problems

      • James S. Byrnes
      Pages 369-386

    3. How to Use the Fourier Transform in Asymptotic Analysis

      • V. Gurarii, J. Steiner, V. Katsnelson, V. Matsaev
      Pages 387-401
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Keywords

About this book

Almost a century ago, harmonic analysis entered a (still continuing) Golden Age, with the emergence of many great masters throughout Europe. They created a wealth of profound analytic methods, to be successfully exploited and further developed by succeeding generations. This flourishing of harmonic analysis is today as lively as ever, as the papers presented here demonstrate. In addition to its own ongoing internal development and its basic role in other areas of mathematics, physics and chemistry, financial analysis, medicine, and biological signal processing, harmonic analysis has made fundamental contributions to essentially all twentieth century technology-based human endeavours, including telephone, radio, television, radar, sonar, satellite communications, medical imaging, the Internet, and multimedia. This ubiquitous nature of the subject is amply illustrated.

The book not only promotes the infusion of new mathematical tools into applied harmonic analysis, but also to fuel the development of applied mathematics by providing opportunities for young engineers, mathematicians and other scientists to learn more about problem areas in today's technology that might benefit from new mathematical insights.

Editors and Affiliations

  • Prometheus Inc., Newport, USA

    James S. Byrnes

  • University of Massachusetts at Boston, Boston, USA

    James S. Byrnes

Bibliographic Information

  • Book Title: Twentieth Century Harmonic Analysis

  • Book Subtitle: A Celebration

  • Editors: James S. Byrnes

  • Series Title: NATO Science Series II: Mathematics, Physics and Chemistry

  • DOI: https://doi.org/10.1007/978-94-010-0662-0

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2001

  • Hardcover ISBN: 978-0-7923-7168-7Published: 30 September 2001

  • Softcover ISBN: 978-0-7923-7169-4Published: 30 September 2001

  • eBook ISBN: 978-94-010-0662-0Published: 06 December 2012

  • Series ISSN: 1568-2609

  • Edition Number: 1

  • Number of Pages: XI, 412

  • Topics: Analysis

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