Real And Complex Clifford Analysis

by Huang, Sha; Qiao, Yu Ying; Wen, Guo Chun

• ISBN13: 9780387245355
• ISBN10: 0387245359
• Format: Hardcover
• Copyright: 2005-12-25
• Publisher: Springer Verlag

Summary

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.

Table of Contents

Preface	ix
General Regular and Harmonic Functions in Real and Complex Clifford Analysis	1	(40)
Real and Complex Clifford Algebra	1	(3)
Cauchy Integral Formula of Regular Functions and Plemelj Formula of Cauchy Type Integrals in Real Clifford Analysis	4	(11)
Quasi-Permutations and Generalized Regular Functions in Real Clifford Analysis	15	(9)
The Chain Rule and the Differentiation Rules of new Hypercomplex Differential Functions in Clifford Analysis	24	(6)
Regular and Harmonic Functions in Complex Clifford Analysis	30	(11)
Boundary Value Problems of Generalized Regular Functions and Hyperbolic Harmonic Functions in Real Clifford Analysis	41	(34)
The Dirichlet Problem of Regular Functions for a ball in Real Clifford Analysis	41	(8)
The Mixed Boundary Value Problem for Generalized Regular Functions in Real Clifford Analysis	49	(11)
A Nonlinear Boundary Value Problem with Haseman Shift for Regular Functions in Real Clifford Analysis	60	(8)
The Dirichlet Problem of Hyperbolic Harmonic Functions in Real Clifford Analysis	68	(7)
Nonlinear Boundary Value Problems for Generalized Biregular Functions in Real Clifford Analysis	75	(30)
A Nonlinear Boundary Value Problem for Biregular Functions in Real Clifford Analysis	75	(12)
Nonlinear Boundary Value Problems for Generalized Biregular Functions With Haseman Shift in Real Clifford Analysis	87	(8)
A Nonlinear Boundary Value Problem for Biregular Function Vectors in Real Clifford Analysis	95	(10)
Boundary Value Problems of Second Order Partial Differential Equations for Classical Domains in Real Clifford Analysis	105	(20)
Harmonic Analysis in Classical Domains for Several Complex Variables	105	(5)
The Dirichlet Problem of Second Order Complex Partial Differential Equations for Classical Domains in Complex Clifford Analysis	110	(7)
A Pseudo-Modified Boundary Value Problem of Second Order Real Partial Differential Equations for a Hyperball in Real Clifford Analysis	117	(8)
Integrals Dependent on Parameters and Singular Integral Equations in Real Clifford Analysis	125	(34)
Cauchy's Estimates of Integrals with One Parameter in Real Clifford Analysis	125	(9)
Three Kinds of Poincare-Bertrand Transformation Formulas of Singular Integrals with a Cauchy's Kernel in Real Clifford Analysis	134	(11)
The Composition Formula and Inverse Formula of Singular Integrals with a Cauchy's Kernel in Real Clifford Analysis	145	(3)
The Fredholm Theory of a Kind of Singular Integral Equations in Real Clifford Analysis	148	(5)
Generalized Integrals and Integral Equations in Real Clifford Analysis	153	(6)
Several Kinds of High Order Singular Integrals and Differential Integral Equations in Real Clifford Analysis	159	(38)
The Hadamard Principal Value and Differential Formulas of High Order Singular Integrals with One Singular Point in Real Clifford Analysis	159	(20)
The Holder Continuity of High Order Singular Integrals in Real Clifford Analysis	179	(5)
Nonlinear Differential Integral Equations including Three Kinds of High Order Singular Integrals of Quasi-Bochner-Martinelli Type in Real Clifford Analysis	184	(5)
A Kind of High Order Singular Integrals of Quasi-Bochner-Martinelli Type With two Singular Points and Poincare-Bertrand Permutation Formulas in Real Clifford Analysis	189	(8)
Relation Between Clifford Analysis and Elliptic Equations	197	(42)
Oblique Derivative Problems for Uniformly Elliptic Equations of Second Order	197	(12)
Boundary Value Problems of Degenerate Elliptic Equations of Second Order	209	(8)
The Schwarz Formulas and Dirichlet Problem in Halfspace and in a Ball	217	(11)
Oblique Derivative Problems for Regular Functions and Elliptic Systems in Clifford Analysis	228	(11)
References	239	(10)
Index	249