Boundary Value Problems For Generalized Hypergenic Functions

Clifford algebra is an algebraic system deeply rooted in geometry,which is an as-sociative but non-exchangeable algebra,known by its founder Clifford as a geometric algebra.Clifford analysis mainly studies the related theories and properties about func-tions which are defined in the Euclidean space and whose values in Clifford algebraic spaces.In recent years,Clifford analysis has been fully developed as the latest analysis branch.The complex boundary value problem is the 20th of the 23 questions raised by the great mathematician Hilbert in his famous lecture at the Paris mathematician conference in 1900.The analytical boundary value problem is an important branch of classical complex analysis and at the same time it is also an important research direction of complex boundary value problems.Based on this,we mainly study the boundary value problems for hypergenic functions and the generalized hypergenic functions in Clifford analysis.This paper is divided into the following three chapters:The first chapter introduces some definitions in Clifford algebra and some lemmas and some theorems;The second chapter mainly discusses the related properties of quasi-Cauchy type integral and boundary value problems for hypergenic function;The third chapter mainly discusses the expression of the generalized hypergenic functions and boundary value problems for the generalized hypergenic functions.