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Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science Volume 1 Foundations

A Monograph Based on Articles of the Founding Authors, Reproduced in Full

  • Book
  • © 2015

Overview

Authors:
  1. Radomir Stankovic

    1. Faculty of Electronic Engineering, Nis, Serbia

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  2. Paul Leo Butzer

    1. Lehrstuhl A für Mathematik, RWTH Aachen, Aachen, Germany

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  3. William R. Wade

    1. Math. and Computer Science, BIOLA University, La Miranda, USA

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  4. Weiyi Su

    1. Mathematics, Nanjing University, Nanjing, China

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  5. Yasushi Endow

    1. Chuo University, Tokyo, Japan

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  6. Sandor Fridli

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

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  7. Boris I. Golubov

    1. Technologies (State University), Moscow Institute of Physical, Moscow, Russia

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  8. Franz Pichler

    1. System Theory, Johannes Kpeler University, Linz, Linz, Austria

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  • A unique development of a field by seven founding authors, together with reproductions of some of their basic papers
  • Applications to dyadic differential equations, approximation theory, etc.
  • Reviews of former and recent results help the reader to get a fast introduction and a rather complete coverage of the area. A separate chapter with open problems should be useful for further research in the field
  • Includes supplementary material: sn.pub/extras

Part of the book series: Atlantis Studies in Mathematics for Engineering and Science (ASMES, volume 12)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xxiv
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  2. Early History of Walsh Analysis

    • William R. Wade
    Pages 1-36

  3. My involvement in Walsh and Dyadic Analysis

    • Franz Pichler
    Pages 37-88

  4. The Origins of the Dyadic Derivative due to James Edmund Gibbs

    • Radomir S. Stanković, Ferenc Schipp
    Pages 89-160

  5. Early Contributions from the Aachen School to Dyadic Walsh Analysis with Applications to Dyadic PDEs and Approximation Theory

    • Paul L. Butzer, Heinrich Josef Wagner
    Pages 161-208

  6. Dyadic Derivative, Summation, Approximation

    • Sándor Fridli, Ferenc Schipp
    Pages 209-234

  7. How I Started My Research in Walsh and Dyadic Analysis

    • Ferenc Schipp
    Pages 235-246

  8. My Involvement with the Dyadic Derivative

    • Kees (C.W.) Onneweer
    Pages 247-313

  9. Hardy Spaces in the Theory of Dyadic Derivative

    • Ferenc Weisz
    Pages 315-346

  10. Term by Term Dyadic Differentiation of Walsh Series

    • William R. Wade
    Pages 347-358

  11. Why I got Interested in Dyadic Differentiation

    • William R. Wade
    Pages 359-441

  12. Dyadic Derivative and Walsh-Fourier Transform

    • Boris I. Golubov
    Pages 443-447

  13. How I started my research in Walsh and dyadic analysis

    • Boris I. Golubov
    Pages 449-452

  14. Back Matter

    Pages 453-455
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Keywords

About this book

Dyadic (Walsh) analysis emerged as a new research area in applied mathematics and engineering in early seventies within attempts to provide answers to demands from practice related to application of spectral analysis of different classes of signals, including audio, video, sonar, and radar signals. In the meantime, it evolved in a mature mathematical discipline with fundamental results and important features providing basis for various applications. The book will provide fundamentals of the area through reprinting carefully selected earlier publications followed by  overview of recent results concerning particular subjects in the area written by experts, most of them being founders of the field, and some of their followers. In this way, this first volume of the two volume book offers a rather complete coverage of the development of dyadic Walsh analysis, and provides a deep insight into its mathematical foundations necessary for consideration of generalizations and applications that are the subject of the second volume. The presented theory is quite sufficient to be a basis for further research in the subject area as well as to be applied in solving certain new problems or improving existing solutions for tasks in the areas which motivated development of the dyadic analysis.

Authors and Affiliations

  • Faculty of Electronic Engineering, Nis, Serbia

    Radomir Stankovic

  • Lehrstuhl A für Mathematik, RWTH Aachen, Aachen, Germany

    Paul Leo Butzer

  • Math. and Computer Science, BIOLA University, La Miranda, USA

    William R. Wade

  • Mathematics, Nanjing University, Nanjing, China

    Weiyi Su

  • Chuo University, Tokyo, Japan

    Yasushi Endow

  • Numerical Analysis, Eötvös Loránd University, Budapest, Hungary

    Sandor Fridli

  • Technologies (State University), Moscow Institute of Physical, Moscow, Russia

    Boris I. Golubov

  • System Theory, Johannes Kpeler University, Linz, Linz, Austria

    Franz Pichler

Bibliographic Information

  • Book Title: Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science Volume 1 Foundations

  • Book Subtitle: A Monograph Based on Articles of the Founding Authors, Reproduced in Full

  • Authors: Radomir Stankovic, Paul Leo Butzer, William R. Wade, Weiyi Su, Yasushi Endow, Sandor Fridli, Boris I. Golubov, … Franz Pichler

  • Series Title: Atlantis Studies in Mathematics for Engineering and Science

  • DOI: https://doi.org/10.2991/978-94-6239-160-4

  • Publisher: Atlantis Press Paris

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Atlantis Press and the author(s) 2015

  • Hardcover ISBN: 978-94-6239-159-8Published: 08 January 2016

  • eBook ISBN: 978-94-6239-160-4Published: 29 December 2015

  • Series ISSN: 1875-7642

  • Series E-ISSN: 2467-9631

  • Edition Number: 1

  • Number of Pages: XXIV, 455

  • Topics: Abstract Harmonic Analysis, Math Applications in Computer Science

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