The Related Boundary Value Problems Of Bihypergenic Function Vectors And Generalized Hypergenic Function Vectors

The properties of functions defined in Euclidean Spaces and evaluated in Clifford algebra are studied in Clifford analysis.Clifford analysis is a generalization of the theory of functions of a complex variable in high dimensional space,and it is of great theoretical significance and application value for the study of equations and operators in high dimensional space.First,the boundary value problem of the bihypergenic function vector and the boundary value problem of the bihypergenic function vector with Haseman displacement and conjugate are studied.Next,the boundary value problem of the generalized hypergenic function vector is studied.Finally,Almansi-type decomposition theorem of bi-k-regular functions is proved.This paper is divided into the following four chapters:The first chapter mainly introduces the preparatory knowledge about this paper;The second chapter mainly studies the boundary value problem of bihypergenic function vector and the boundary value problem of bihypergenic function vector with Haseman displacement and conjugate;The third chapter mainly discusses the boundary value problem of the generalized hypergenic function vector;The fourth chapter gives the Almansi-type decomposition theorem of bi-k-regular function.