Study On Quasi Cauchy Type Integral And Boundary Value Problems With B-M Kernal In Complex Clifford Analysis

This paper obtains the Plemelj formula of quasi Cauchy type integral with B-M kernel on bounded domain,the Cauchy's integral formula and a series of theorems on unbounded domain in half space and unbounded domains with nonempty open sets in the complementary set,which are of great significance for further study of boundary value problems in the future.This paper is divided into six parts.The first part is the introduction,which expounds the research background,research status and main research contents of this paper.The second part is the preliminary knowledge,gives some relevant theoretical basis,and introduces the complex Clifford algebra called Cl0,n(C),the basic algorithm,as well as the related concepts in complex Clifford analysis,such as generalized polar coordinate transformation,calculus,Dirac operator,complex regular function,Holder continuous function.The third part,The Plemelj formula of quasi Cauchy type integral is obtained by using the Cauchy's integral formula of complex right regular function with B-M kernal on bounded domain ? in complex Clifford analysis.For any z0?(?)?,#12The fourth part,we modify the B-M kernel on the bounded domain,construct the modified B-M kernel,extend the bounded domain to unbounded domain D in half space,and obtain the Cauchy's integral formula.For any z?D,#12#12The fifth part,we further modify the B-M kernel on the bounded domain,extend the bounded domain to the unbounded domain U with nonempty open set in the complementary set and obtain the Cauchy's integral formula and a series of properties.Set u as the point in the remainder of U,for any z?U,#12#12The sixth part is the conclusion,which summarizes the work of this paper and looks forward to the next research.