K-解析函数的Riemann边值问题  

Riemann's Boundary Value Problem of K-Analytic Functions

作　　者：张建元[1] 赵书芬[1,2] 韩艳[1] 

机构地区：[1]昭通学院数学与统计学院,云南昭通657000 [2]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《应用数学和力学》2014年第7期805-814,共10页Applied Mathematics and Mechanics

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

摘　　要：引入了(分片)K-解析函数和Cauchy型K-积分的概念.利用K-对称变换的方法研究了Cauchy型K-积分的某些性质,然后借助函数在曲线上的指标与这些Cauchy型K-积分的性质,得到了K-解析函数类中的Riemann边值问题的可解条件和解的表达式以及它们与指标之间的关系.而解析函数和共轭解析函数都是K-解析函数的特例,文中所得结果,推广了解析函数和共轭解析函数中的相应结论.First, the concepts of the （piecewise） K-analytic function and the Cauchy type K-in- tegral were introduced, and some properties of the Cauchy type K-integral were studied through K-sylmlletry transformation. Then, with the function index of the curve and the properties of the Cauchy type K-integral, the solvable conditions and the solution expressions for the Rie- mann＇ s boundary value problem of the K-analytic flmction as well as the relationship between the solutions and the index were obtained. Since both the analytic functions and the conjugate analytic functions are special cases of the K-analytic functions, the present conclusions general- ize many known related results of them.

关 键 词：Cauchy型K-积分 (分片)K-解析函数 K-对称变换 边界值公式 RIEMANN 边值问题 指标 

分 类 号：O174.55[理学—数学] O175.5[理学—基础数学]