Cauchy Integral Formula Of Bihypergenic Functions And The Related Theories

In the real Clifford analysis,some properties are studied about functions defined in the real vector space Rn.which are valued in the Clifford algebra.Real Clifford analy-sis can be seen as the high-dimensional extension of real analysis,complex analysis and quaternion analysis.Cauchy integral formulas,Plemelj formulas and the related prop-erties of the right hypergenic function and the bihypergenic function in the real Clifford analysis are studied in this paper.Based on this,the existence and uniqueness of solutions to the linear boundary value problem of the bihypergenic function are demonstrated by using the principle of compression mapping.This paper is divided into the following four chapters:Some definitions and the relevant lemmas of the Clifford analysis are introduced in chapter 1;The Cauchy integral formula and the main related properties of the right hy pergenic quasi-Cauchy type integral are mainly discussed in chapter 2;The Cauchy integral formula of the bihy pergenic function and the related Plemelj formula are mainly considered in chapter 3;The linear boundary value problem of the bihypergenic function is mainly studied in chapter 4.