Z2不变的C∞函数芽的典型形式

数学物理学报 ›› 1999, Vol. 19 ›› Issue (5): 537-540.

Z2不变的C∞函数芽的典型形式

(黔南师专数学系贵州都匀 558000)
贵州民族学院数学系 |贵州 550025)

出版日期:1999-12-05 发布日期:1999-12-05

The Canonical Form of Z2 invariant C&infin|Function Germs

(Deptartment of Mathematics Qiannan Teachers College, Guizhou Duyun 558000)
(Deptartment of Mathematics Guizhou Institute for Nationalities, Guiyang 550025)

Online:1999-12-05 Published:1999-12-05

摘要/Abstract

摘要：

Whitney关于偶函数的结果给出了一个变元且在Z₂群{±1}下不变的C^∞函数芽的典型形式：如果f∈E₁且f(-x)=f(x),则存在h∈E₁使得f(x)=h(x²).该文将借助Malgrange预备定理和有关的计算，得出Rⁿ在原点且在群{±I_n}下不变的C^∞函数芽的典型形式.

关键词: Malgrange预备定理, Z₂不变, 典型形式.

Abstract:

The result of Whitney on even functions gives the canonical form of invariant C∞ function germs under Z₂ group {±1} in one variable: If f∈E₁ and f(-x)=f(x),then there exists h∈E₁ such that f(x)=h(x²).In this paper, by means of Malgrange preparation theorem and the related computation, the authors obtain the canonical from of invariant C∞ function germs under group {±I_n} in Rⁿ at origin.

Key words: Malgrange preparation theorem, Z₂ invariant, canonical form.

中图分类号:

58C27

岑燕斌吴兴玲. Z2不变的C∞函数芽的典型形式[J]. 数学物理学报, 1999, 19(5): 537-540.

Cen Yanbin Wu Xinling. The Canonical Form of Z2 invariant C&infin|Function Germs[J]. Acta mathematica scientia,Series A, 1999, 19(5): 537-540.