K-解析函数的Hilbertert边值问题  

Hilbert Boundary Value Problem for K-analytic Function

作　　者：张建元[1] 张毅敏[1] 黄永[1] 韩艳[1] 罗雪梅 张昕 ZHANG Jian-yuan ZHANG Yi-min HUANG Yong HAN Yan LUO Xue-mei ZHANG Xin(Department of Mathematics, Zhaotong University, Zhaotong 657000, China Zhaotong Finance Bureau, Zhaotong 657000, China Zhaotong Statistics Bureau, Zhaotong 657000, China)

机构地区：[1]昭通学院数学与统计学院,云南昭通657000 [2]昭通市财政局,云南昭通657000 [3]昭通市统计局,云南昭通657000

出　　处：《数学的实践与认识》2016年第24期254-260,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11061028);云南省教育厅科学研究基金资助项目(2012Y435;2013Y578)

摘　　要：定义和讨论了K-解析函数在典型域S^+={z:|z(k)|<1}外的K-对称扩张函数,利用它把K-解析函数的Hilbert边值问题转化为Riemann边值问题,得到了K-解析函数类F(D(k))中Hilbert边值问题与Dirichlet边值问题的可解条件及其解的表达式.而解析函数和共轭解析函数都是K-解析函数的特例,所得结果,包含了解析函数和共轭解析函数中的相应结论.In this paper, K-symmetric extended function, a special case of K-analytic function outside of the classical domain S＋ = {z ： ｜z（k）｜ 〈 1}, is defined and studied. When it is used to convert Hilbert boundary value problem into Riemann boundary value problem, we obtain the solvable conditions and solution expression of Hilbert boundary value problem and Dirichlet boundary value problem of K-analytic function F（D（k））. As analytic functions and conjugate analytic functions are a special case of K-analytic functions, the conclusions included the corresponding results of analytic functions and conjugate analytic functions.

关 键 词：K-解析函数 典型域 K-对称扩张函数 HILBERT边值问题 DIRICHLET边值问题 Schwarz积分公式. 

分 类 号：O174[理学—数学]