Riemann-Hilbert Problems for Monogenic Functions on Upper Half Ball of R^4
Riemann-Hilbert Problems for Monogenic Functions on Upper Half Ball of R^4
复制标题
R^4 上半球上单元函数的黎曼-希尔伯特问题
DOI：
10.1007/s00006-017-0789-8
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发表时间：
2017
影响因子：
1.5
通讯作者：
Kähler Uwe
中科院分区：
文献类型：
--
作者：
Ku Min;Wang Ying;He Fuli;Kähler Uwe
在本文中，我们有兴趣寻找解决方案的Riemann-Hilbert边值问题，简称Riemann-Hilbert问题，与可变系数的情况下，轴向单演函数定义在上半单位球中心的原点在四维欧氏空间。我们的主要思想是将四维欧氏空间上半单位球上轴单演函数的Riemann-Hilbert问题转化为复平面上半单位圆盘上解析函数的Riemann-Hilbert问题。此外，我们将所得结果推广到扰动广义Cauchy-Riemann方程的轴对称零解。
In this paper we are interested in finding solutions to Riemann–Hilbert boundary value problems, for short Riemann–Hilbert problems, with variable coefficients in the case of axially monogenic functions defined over the upper half unit ball centred at the origin in four-dimensional Euclidean space. Our main idea is to transfer Riemann–Hilbert problems for axially monogenic functions defined over the upper half unit ball centred at the origin of four-dimensional Euclidean spaces into Riemann–Hilbert problems for analytic functions defined over the upper half unit disk of the complex plane. Furthermore, we extend our results to axially symmetric null-solutions of perturbed generalized Cauchy–Riemann equations.