实系数克里弗德解析函数的零点集合

数学物理学报 ›› 2011, Vol. 31 ›› Issue (5): 1160-1166.

实系数克里弗德解析函数的零点集合

杨燕¹|钱涛²

1.中山大学数学与计算科学学院广州 510275;
2.澳门大学科技学院数学系澳门

收稿日期:2009-08-05 修回日期:2010-12-01 出版日期:2011-10-25 发布日期:2011-10-25
基金资助:
国家自然科学基金青年基金(10901166)、中山大学青年教师基金、澳门大学基金 (cativo: 7560)和澳门FDCT(014/2008/A1)资助

Zero-sets of Clifford Analytic Functions with Real Coefficients

YANG Yan¹, QIAN Tao²

1.School of Mathematics and Computational Science, Sun Yat-Sen University, Gungzhou 510275;
2.Department of Mathematics, Faculty of Science and Technology, University of |Macau, Macau

Received:2009-08-05 Revised:2010-12-01 Online:2011-10-25 Published:2011-10-25
Supported by:
国家自然科学基金青年基金(10901166)、中山大学青年教师基金、澳门大学基金 (cativo: 7560)和澳门FDCT(014/2008/A1)资助

摘要/Abstract

摘要：

该文证明了实系数克里弗德解析函数f的零点集合包含两种情况: 孤立的实零点和球形共轭零点. 另外, 还给出了计算此零点的方法. 对于任意的向量A∈R¹_m, 该文也研究了f(x)= A的根的集合.

关键词: 克里弗德代数, 零点集合

Abstract:

In this note it is proved that the zero set of any Clifford analytic function f with real coefficients is the disjoint union of real isolated zeroes and the spherical conjugate ones. What is more, a technique for computing the zeroes is presented. The authors also find the preimages f^-1(A) for any paravector A.

Key words: Clifford algebra, Zero sets

中图分类号:

30G35

杨燕, 钱涛. 实系数克里弗德解析函数的零点集合[J]. 数学物理学报, 2011, 31(5): 1160-1166.

YANG Yan, QIAN Tao. Zero-sets of Clifford Analytic Functions with Real Coefficients[J]. Acta mathematica scientia,Series A, 2011, 31(5): 1160-1166.

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