Riemann Boundary Value Problems on the Sphere in Clifford Analysis
Riemann Boundary Value Problems on the Sphere in Clifford Analysis
复制标题
DOI：
10.1007/s00006-011-0308-2
复制
发表时间：
2012-06
影响因子：
1.5
通讯作者：
M. Ku;U. Kähler;Daoshun Wang
中科院分区：
文献类型：
--
作者：
M. Ku;U. Kähler;Daoshun Wang
本文提出并研究了一类多项式单演函数的Riemann边值问题，即多项式广义Cauchy-Riemann方程的零解。利用Fischer型分解和多项式单演函数的Clifford微积分，得到了这类边值问题在球面上解的显式表达式.作为特例，分别给出了经典多解析函数和亚解析函数相应边值问题的解。
We present and study a type of Riemann boundary value problems (for short RBVPs) for polynomially monogenic functions, i.e. null solutions to polynomially generalized Cauchy-Riemann equations, over the sphere of. Making use of Fischer type decomposition and the Clifford calculus for polynomially monogenic functions, we obtain explicit expressions of solutions of this kind of boundary value problems over the sphere of. As special cases the solutions of the corresponding boundary value problems for classical polyanalytic functions and metaanalytic functions are derived respectively.