扇形环上多解析方程的Schwarz边值问题
Schwarz boundary value problems for polyanalytic equation in a sector ring
摘要：
本文首先利用适当的共形映射给出了一般扇形环上的一个修正的Schwarz-Pompeiu公式，并得到了Cauchy-Riemann方程Schwarz问题的显式解.此外，还引入了一类积分算子及其性质。最后，利用这些算子，分别研究了非齐次多解析方程和广义多解析方程的Schwarz问题。
英文摘要：
In this article,we first give a modified Schwarz-Pompeiu formula in a general sector ring by proper conformal mappings, and obtain the solution of the Schwarz problem for the Cauchy-Riemann equation in explicit forms. Furthermore, a class of integral operators is introduced together with their properties. Finally, by virtue of these operators, Schwarz problems for a inhomogeneous polyanalytic equation and for a generalized polyanalytic equation are investigated, respectively.
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