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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.
This book is intended for mathematicians studying function theory.
Content Level »Research
Keywords »Boundary value problem - Complex analysis - Integral equation - algebra - partial differential equation
General Regular and Harmonic Functions in Real and Complex Clifford Analysis.- Boundary Value Problems of Generalized Regular Functions and Hyperbolic Harmonic Functions in Real Clifford Analysis.- Nonlinear Boundary Value Problems for Generalized Biregular Functions in Real Clifford Analysis.- Boundary Value Problems of Second Order Partial Differential Equations for Classical Domains in Real Clifford Analysis.- Integrals Dependent on Parameters and Singular Integral Equations in Real Clifford Analysis.- Several Kinds of High Order Singular Integrals and Differential Integral Equations in Real Clifford Analysis.- Relation Between Clifford Analysis And Elliptic Equations.