【作者】 闫川；

【导师】 杨丕文；

【作者基本信息】 四川师范大学 ， 应用数学， 2010， 硕士

【摘要】 本文利用复分析的方法讨论了复平面上的k-正则函数的某些边值问题.在第一章中给出了k正则函数的一类Riemann边值问题及非齐次k阶方程akw/azk=f的Riemann边值问题的提法,讨论了该边值问题的可解条件和解的表示.使用类似于[7]的方法,通过将k-函数的Riemann边值问题转化为解析函数的Riemann边值问题,并利用文[7]的结论得出其相关的可解条件和解的表达式.在第二章中给出了无穷直线上含参变未知函数的k-正则函数的Riemann边值问题的提法,讨论了该边值问题的可解条件和解的表示.更多还原

【Abstract】 In this paper,some boundary-value problems of k-regular function on complex plane are discussed by the tool of complex analysis.In chapter one,the Riemann boundary-value problems of k-regular func-tion and the equation of n-order such as (?)=f are obtained. the solv-able conditions and representations of solutions are discussed. The Riemann boundary-value problems of k-regular functions are transformed into the Rie-mann boundary-value problems of analytic functions in a ways like [7].The relative solvable conditions and expressions of solutions are investigated in a way like [7].In the second chapter,the Riemann boundary-value problems of k-regular functions with unknown function in infinite line are examined. The solvable conditions and expressions of solutions of this boundary-value problems are also discussed.更多还原