Integral representations in complex, hypercomplex and Clifford analysis

作     者：Begehr, H 

作者机构：Free Univ Berlin Inst Math 1 D-14195 Berlin Germany 

出 版 物：《INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS》 (积分变换与特殊函数)

年 卷 期：2002年第13卷第3期

页      面：223-241页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Cauchy-Pompeiu representation Poisson equation Bitzadse equation complex higher order partial differential equations orthogonal decomposition of L-2(D C) polyharmonic functions polyanalytic functions second order representations in bidomains higher order Cauchy-Pompeiu representations in Clifford Analysis 

摘      要：Iterating the Pompeiu integral operator leads to area integral operators being right inverses to proper powers of the Cauchy-Riemann differential operator. These integral operators serve to solve boundary value problems for differential equations the leading term of which is some power of the Cauchy-Riemann operator. This situation in investigated also for products of powers of the Cauchy-Riemann operator and its complex conjugate. Besides the complex cases of one and of several complex variables the consideration can be extended to the hypercomplex and actually is extended to the Clifford analysis case. The generalized Cauchy-Pompeiu formula is used to orthogonally decompose the set L-2(D,C) with respect to polyanalytic and polyharmonic functions.