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Topics in Clifford Analysis

Special Volume in Honor of Wolfgang Sprößig

  • Swanhild Bernstein
Book

Part of the Trends in Mathematics book series (TM)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Clifford Analysis Theories

    1. Front Matter
      Pages 1-1
    2. Fred Brackx, Hennie De Schepper, Roman Lávička, Vladimir Souček
      Pages 3-23
    3. Sirkka-Liisa Eriksson, Heikki Orelma
      Pages 25-52
  3. Applications to Elliptic Partial Differential Equations

    1. Front Matter
      Pages 103-103
    2. Juan José Marín, José María Martell, Dorina Mitrea, Irina Mitrea, Marius Mitrea
      Pages 105-124
    3. Briceyda B. Delgado, R. Michael Porter
      Pages 125-140
    4. Swanhild Bernstein, Sandra Schufmann
      Pages 191-218
  4. Monogenic Polynomials and Numerical Methods

  5. Differential Geometry

    1. Front Matter
      Pages 277-277
    2. Viktor Abramov, Olga Liivapuu
      Pages 279-311
    3. Vladimir V. Kisil, James Reid
      Pages 313-330
    4. Chao Ding, Raymond Walter, John Ryan
      Pages 347-380
    5. Craig A. Nolder
      Pages 381-394
    6. Roman Lávička
      Pages 395-403
    7. Yakov Krasnov, Vladimir G. Tkachev
      Pages 405-436
  6. Discrete Clifford Analysis

About this book

Introduction

Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Sprößig’s work was the application of quaternionic analysis to elliptic differential equations and boundary value problems. Over the years, Clifford analysis has become a broad-based theory with a variety of applications both inside and outside of mathematics, such as higher-dimensional function theory, algebraic structures, generalized polynomials, applications of elliptic boundary value problems, wavelets, image processing, numerical and discrete analysis.

The aim of this volume is to provide an essential overview of modern topics in Clifford analysis, presented by specialists in the field, and to honor the valued contributions to Clifford analysis made by Wolfgang Sprößig throughout his career.

Keywords

Clifford analysis quaternionic analysis hypercomplex analysis elliptic partial differential equations monogenic polynomials numerical analysis differential geometry discrete Clifford analysis

Editors and affiliations

  • Swanhild Bernstein
    • 1
  1. 1.Institut für Angewandte AnalysisTU Bergakademie FreibergFreibergGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-23854-4
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-23853-7
  • Online ISBN 978-3-030-23854-4
  • Series Print ISSN 2297-0215
  • Series Online ISSN 2297-024X
  • Buy this book on publisher's site
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