四元数分析中的双正则函数的性质以及边值问题

The Property and the Boundary Value Problems for Biregular Function in Quaternionic Analysis

首先研究了四元数中双正则函数的一些性质,如Pompeiu公式、Cauchy积分公式等.在双圆柱区域上,讨论了δ_z^2w=f的Dirichlet边值问题,给出了问题的可解性条件和解得积分表达式.

In this paper,we study the property for biregular funtions in quaternionic analysis. Then, we dicuss the Dirichlet boundary value problems about d2zω = f in bicylinder area, and the solvable conditions and the integral expressions of the generalsolution are given.