Research On Some Boundary Value Problems In Clifford Analysis And Related Problems Of M(?)bius Transformation

Clifford analysis is the generalization of single complex analysis in higher dimensional space,and it has very important theoretical significance and application value for the study of equations and operators in higher dimensional space.Mobius transformation theory is one of the important research contents of Clifford analysis.In this paper,the boundary value problems of generalized bihypergenic functions and the composite problems of hyperbolic harmonic functions,left-infra-hypermonogenic functions with conjugates,infra-hypermonogenic functions and Clifford Mobius transformation are solved respectively.This paper is mainly divided into the following four chapters.In the first chapter,the Plemelj formula and the boundary value problem of the generalized bihypergenic function in Clifford algebra Cln+1,0(R)are studied.In the second chapter,the composite problem of the hyperbolic harmonic function and Clifford M(?)bius transformation in Clifford algebra Cl0,n(R)is discussed.In the third chapter,the composite problems of the left-inframonogenic function with conjugate,the left-infra-hypermonogenic function with conjugate and Clifford Mobius transformation in Clifford algebra Cl0,n(R)are studied respectively.In the fourth chapter,the composite problems of the inframonogenic function,the infra-hypermon-ogenic function and Clifford Mobius transformation in Clifford algebra Cl0,n-1(R)are given respectively.