k-超正则函数及其相关函数的性质

数学物理学报 ›› 2009, Vol. 29 ›› Issue (3): 716-726.

k-超正则函数及其相关函数的性质

(1. 河北师范大学数学与信息科学学院 |石家庄 050016|2. 河北工程大学 |理学院 |河北邯郸 056038)

收稿日期:2007-11-19 修回日期:2009-03-10 出版日期:2009-06-25 发布日期:2009-06-25
基金资助:
国家自然科学数学天元基金(A0324610)和河北省自然科学基金(102129)资助

Properties of k-Hypermonogenic Functions and Their Relative Functions

(1. College of Mathematics and Information Science, Hebei Normal University, Shi Jiazhuang 050016|
2. College of Science, Hebei University of Engineering, Handan 056038)

Received:2007-11-19 Revised:2009-03-10 Online:2009-06-25 Published:2009-06-25
Supported by:
国家自然科学数学天元基金(A0324610)和河北省自然科学基金(102129)资助

摘要/Abstract

摘要：

给出了k -超正则函数的开拓定理和唯一性定理，由唯一性定理证明了超正则函数列的内闭一致收敛性; 由k -超正则函数的P 部和Q 部满足的两个微分方程，讨论了此方程与k -超正则函数及其相关函数的关系.

关键词: k-超正则函数, k -超调和函数, 开拓定理, 唯一性定理, k -超正则函数的 P 部和 Q 部

Abstract:

In the first part of this paper, the authors show the extension theorem and uniqueness theorem of k-hypermonogenic functions. What is more, by the uniqueness theorem, the authors prove the inner-closed uniform convergence of sequence of hypermonogenic functions. In the second part of this paper, as P-part and Q-part of k-hypermonongenic functions satisfy two equations, the authors discuss the relationship between these two equations and k-hypermonogenic functions and their relative functions.

Key words: k-Hypermonogenic function, k-Hyperbolic Harmonic function, Extension theorem, Uniqueness theorem, the P-part and Q-part of k-Hypermonogenic function

中图分类号:

30G99

袁洪芬, 乔玉英. k-超正则函数及其相关函数的性质[J]. 数学物理学报, 2009, 29(3): 716-726.

YUAN Hong-Fen, JIAO Yu-Ying. Properties of k-Hypermonogenic Functions and Their Relative Functions[J]. Acta mathematica scientia,Series A, 2009, 29(3): 716-726.

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