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Real and Complex Clifford Analysis

  • Book
  • © 2006

Overview

Authors:
  1. Sha Huang

    1. Hebei Normal University, Shijiazhuang, People’s Republic of China

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  2. Yu Ying Qiao

    1. Hebei Normal University, Shijiazhuang, People’s Republic of China

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  3. Guo Chun Wen

    1. Peking University, Beijing, People’s Republic of China

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  • Systematic exposition of many results previously published only in Chinese
  • Unlike most books on the subject, considers both real and complex Clifford analysis rather than just real Clifford analysis
  • Considers not only regular (i.e., monogenic) functions but also generalized regular functions
  • Includes supplementary material: sn.pub/extras

Part of the book series: Advances in Complex Analysis and Its Applications (ACAA, volume 5)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-x
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  2. General Regular and Harmonic Functions in Real and Complex Clifford Analysis

    Pages 1-40

  3. Boundary Value Problems of Generalized Regular Functions and Hyperbolic Harmonic Functions in Real Clifford Analysis

    Pages 41-73

  4. Nonlinear Boundary Value Problems for Generalized Biregular Functions in Real Clifford Analysis

    Pages 75-103

  5. Boundary Value Problems of Second Order Partial Differential Equations for Classical Domains in Real Clifford Analysis

    Pages 105-124

  6. Integrals Dependent on Parameters and Singular Integral Equations in Real Clifford Analysis

    Pages 125-158

  7. Several Kinds of High Order Singular Integrals and Differential Integral Equations in Real Clifford Analysis

    Pages 159-195

  8. Relation Between Clifford Analysis And Elliptic Equations

    Pages 197-237

  9. Back Matter

    Pages 239-251
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Keywords

About this book

Clifford analysis, a branch of mathematics that has been developed since about 1970, has important theoretical value and several applications. In this book, the authors introduce many properties of regular functions and generalized regular functions in real Clifford analysis, as well as harmonic functions in complex Clifford analysis. It covers important developments in handling the incommutativity of multiplication in Clifford algebra, the definitions and computations of high-order singular integrals, boundary value problems, and so on. In addition, the book considers harmonic analysis and boundary value problems in four kinds of characteristic fields proposed by Luogeng Hua for complex analysis of several variables. The great majority of the contents originate in the authors’ investigations, and this new monograph will be interesting for researchers studying the theory of functions.

Reviews

From the reviews:

"It deals with boundary value problems and singular integrals using Clifford analytic methods. One of its merits is the accessibility in English of several results published up to now only in Chinese. … The references include articles and books by 90 authors. … this is an interesting book … it may be recommended to the specialist." (Klaus Habetha, Zentrablatt MATH, Vol. 1096 (22), 2006)

Authors and Affiliations

  • Hebei Normal University, Shijiazhuang, People’s Republic of China

    Sha Huang, Yu Ying Qiao

  • Peking University, Beijing, People’s Republic of China

    Guo Chun Wen

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