有关K-调和函数的一些性质  

Some properties of K-harmonic function

作　　者：何萍[1] 张邵斌 

机构地区：[1]红河学院数学学院,云南蒙自661199

出　　处：《西南民族大学学报（自然科学版）》2016年第1期92-95,共4页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金(11301160);云南省自然科学基金(2013FZ116);红河学院科研基金项目(XJ14Y05)

摘　　要：复变函数理论被广泛地应用到空气动力学、理论物理、电子技术、热学等许多方面.文章根据K-laplace算子和K-调和函数的定义,运用偏导数的数学思想,讨论了一对共轭K-调和函数的乘积仍为K-调和函数;K-调和函数的线性组合仍是K-调和函数.同时,获得K-解析函数的虚部是此函数的实部的共轭K-调和函数,而共轭K-调和函数也可以构造K-解析函数.所得结论是解析函数与调和函数理论的应用.The complex function theory is widely used in many aspects such as aerodynamics, theoretical physics, electronic technology. This paper is based on the definitions of K -laplace operator and K - harmonic function, uses the partial derivative in mathematics,and discusses the fact that the product of a pair of conjugate K - harmonic functions is K - harmonic func- tions, and that the linear combinations of K - Harmonic function are K - Harmonic function. At the same time,it proves that the imaginary part of K - analytic function is conjugate K - Harmonic function of real part of the K - analytic function, and that K - analytic functions are constructed by the conjugate K - Harmonic function. The conclusion is the application of analytic func- tion and harmonic function theory.

关 键 词：K-laplace算子 K-调和函数 K-解析函数 Cauchy—Riemann-K方程 

分 类 号：O174.5[理学—数学]