On the Integral Representation of Spherical k-Regular Functions in Clifford Analysis
On the Integral Representation of Spherical k-Regular Functions in Clifford Analysis
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DOI：
10.1007/s00006-008-0067-x
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发表时间：
2009-02
影响因子：
1.5
通讯作者：
Ku Min;Du Jinyuan
中科院分区：
文献类型：
--
作者：
Ku Min;Du Jinyuan
研究了单位球上球面（Atiyah-Singer） Dirac算子局部定义多项式形式迭代应用的零解；一般Clifford代数中的函数，这里称为球正则函数。构造了核函数，得到了球正则函数的积分表示公式和Cauchy积分公式，并应用于高阶非齐次球面（Atiyah-Singer） Dirac方程的弱解。特别地，我们得到了非齐次球面泊松方程Δsg=f的弱解。
We study the null solutions of iterated applications of the spherical (Atiyah-Singer) Dirac operatoron locally defined polynomial forms on the unit sphere of; functions valued in the universal Clifford algebra, here called sphericalk-regular functions. We construct the kernel functions, get the integral representation formula and Cauchy integral formula of sphericalk-regular functions, and as applications, the weak solutions of higher order inhomogeneous spherical (Atiyah-Singer) Dirac equations. We obtain, in particular, the weak solution of an inhomogeneous spherical Poisson equation Δsg=f.