The P-B Transformation Formula Of Quasi-Cauchy Type Integral With Hyper-monogenic Kernel In Clifford Analysis

Clifford algebra An(R)is an associative and incommutable high-dimensional algebra for multiplication.Clifford analysis mainly studies the properties of functions defined on the Euclidean space Rn+l and valued in Clifford algebra.It contains monogenic functions and hyper-monogenic f’unctions,which are the generalization of holomorphic functions of complex variable in high-dimensional space.Monogenic function is the generalization of holomorphic function in Euclidean metric.It is the fundamental solution of Dirac opera-tor (?).While hyper-monogenic function is the generalization of holomorphic function in non-Euclidean mel It is the f’undamental solution of’ the modified Dirac operator Mn-1 = D +(n-1)Q’/Xn.The P-B transf’ormation formula of Cauchy type integral plays an important role in classical f’unctional theory.Hence it is necessary to study the P-B transf’ormation f’ormula of quasi-Cauchy type integral with hyper-monogenic kernelThis thesis studies the transformation problem of quasi-Cauchy type integral with hyper-monogenic kernel.The repeated integral is decomposed into three types of singular integral with hyper-monogenic kernel:the singular integral with two E kernels、the singular int egral with E kernel and M kernel and the singular integral with two M kernels.It discusses the properties of some integrals and the transformation formulas of singular integral with hyper-monogenic kernel.Based on this.it obtains the P-B transf’ormation formula of quasi-Cauchy type integral with hyper-monogenic kernelThis thesis consists of four chaptersIn Chapter 1,it introduces the fundamental structure and algorithm of Clifford algebra.It also gives the related definitions and lemmasIn Chapter 2,the repeated integral with hyper-monogenic kernel is decomposed into four singular integrals.After We discuss the properties of some integralsIn Chapter 3,it proves the transformation formulas of the singular integral with two E kernels、the singular integral with E kernel and M kernel and the singular integral with two M kernels respectivelyIn Chapter 4,we get the P-B transformation formula of quasi-Cauchy type singular integral with hyper-monogenic kernel.