Boundary Value Problems For Hypergenic Function Vector In Clifford Analysis

It is to mainly study the properties and the related theory of the functions which are defined on real vector space Rn and valued on the Clifford algebra.Clifford analysis is a generalization of complex analytic function theory with one variable in high dimensional space,and it is widely used in many branches of mathematics.In real analysis and complex analysis,it is of great significance to study the existence,uniqueness and the expression of the solution to the boundary value problems for the functions,and it plays an important role in modern science and technology production.Boundary value problems for hypergenic function vectors in Clifford analysis is dis-cussed in this paper.By studying the properties of hypergenic function vector space and discussing Cauchy integral and Plemelj formula for hypergenic function vectors,and so on,further using Schauder fixed point principle the existence of the solution to the non-linear boundary value problems for hypergenic function vectors are discussed,and then the existence and the uniqueness of the solution to the linear boundary value problems for hypergenic function vectors with the help of compression mapping are proved.On the basis of this,linear and nonlinear boundary value problems for hypergenic function vec-tors with displacement and conjugate value in Clifford analysis are studied.This paper is divided into three chapters:In chapter 1,the preliminary knowledge and several important theorems and lemmas which we needed are given.In chapter 2,the related properties boundary value problems for hypergenic function vectors are mainly studied.In chapter 3,the boundary value problems for hypergenic function vectors with displacement and conjugate value are studied.