The Conditions of Equivalence of a Class Germs of C~∞ Functions on Banach Spaces

The Conditions of Equivalence of a Class Germs of C~∞ Functions on Banach Spaces

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摘要 In this paper,we prove the converse of gem is right equivalent is also true in[1] and[2],obtain the necessary and sufficient conditions of equivalence of a class gems of C∞ function on Banach spaces.

作者 CEN Yan-bin LIU Wen-wu CEN Yi-gang

机构地区 Department of Mathematics School of Computer and InformatiOn Technology

出处《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第2期223-228,共6页 数学季刊（英文版）

基金 Supported by the National Science Foundation of China（60802045） Supported by the Science and Technology Foundation of Guizhou（20052004） Supported by the Science Foundation of Qiannan Normal College for Nationalities

关键词 Banach space converse theorem Frodholm gem right equivalent implicit function Banach 空间；交谈定理；Frodholm 宝石；恰好相等；含蓄的功能；

分类号 O186.33 [理学—基础数学]

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1MARTINET Jean. Singularities of Smooth Functions and Maps: London Mathematical Society Lecture Note Series[M]. Cambridge and New York: Cambridge University Press, 1982: 45, 155.
2GROMOLL D, MEYER W. On differentiable functions with isolated critical points[J]. Topology, 1969, 8: 361-369.
3MAGUNUS R J. On universal unfolding of certain real functions on a Banach space[J]. Math Proc Camb Phil Soc, 1977, 81: 91-95.
4DIEUDONNE J. Foundation of Modern Analysis[M]. New York: Academic Press, 1969: 102-103, 270.
5GUAN Zhao-zhi, ZHANG Gong-qing, FENG De-xing. Introduction of Linear Functional Analysis[M]. ShanghalShanghal Science and Technology Press, 1979: 107, 112.
6XIA Dao-xing, WU Zhuo-ren, YAN Shao-zong, et al. Real Variable Function Theory and Functional Analysis[M]. Beijing: People's Education Press, 1979: 168, 172.
7MAGNUS R. J. Universal unfolding in Banach space: reduction and stability[J]. Math Proc Camb Phil Soc, 1979, 86: 41-45.
8GOLUBITSKY M, GUILLEMEN V. Stable Mappings and Their Singularities: GTM 14[M]. New York Springer-Verlag, 1973.

1余立,张国滨.Notes on Smooth Map Germs[J].Chinese Quarterly Journal of Mathematics,1995,10(4):114-119.
2熊剑飞.On the Universal Unfoldings of C~∞ Map Germs Under Some Subgroups of A and K[J].Chinese Quarterly Journal of Mathematics,1995,10(4):105-113.
3Changmei SHI,Donghe PEI.Weak Finite Determinacy of Relative Map-Germs[J].Chinese Annals of Mathematics,Series B,2014,35(6):991-1000. 被引量：2
4Xiong Jianfei Institute of Applied Mathematics Qingdao University, 266071 China.Classification of (2, 2)-Stable Unfoldings of Map Germs with Codimensions (?) 4[J].Acta Mathematica Sinica,English Series,1996,12(4):415-432. 被引量：1
5CHEN LIANG,SUN WEI-ZHI,PEI DONG-HE.Contact Finite Determinacy of Relative Map Germs[J].Communications in Mathematical Research,2010,26(1):1-6. 被引量：2
6刘恒兴,张敦穆.V-BILIPSCHITZ DETERMINACY OF WEIGHTED HOMOGENEOUS ANALYTIC FUNCTION-GERMS ON WEIGHTED HOMOGENEOUS REAL ANALYTIC VARIETIES[J].Acta Mathematica Scientia,2010,30(4):1249-1256. 被引量：1
7熊剑飞,邹建成.CLASSIFICATIONS OF (2,1)-STABLE AND (1,2)-STABLE UNFOLDINGS OF MAP GERMS WITH CODIMENTION≤3[J].Acta Mathematica Scientia,2000,20(2):199-205.
8李兵,李养成.Local classification of stable geometric solutions of systems of quasilinear first-order PDE[J].Science China Mathematics,2002,45(9):1163-1170. 被引量：1
9LIU Heng-xing,ZHANG Dun-mu.Finite Indeterminacy of Homogenous Polynomial Germs under Some Subgroups R_(I_r) of R[J].Wuhan University Journal of Natural Sciences,2005,10(5):803-807. 被引量：1
10MOK Ngaiming,NG Sui Chung.Second fundamental forms of holomorphic isometries of the Poincar disk into bounded symmetric domains and their boundary behavior along the unit circle[J].Science China Mathematics,2009,52(12):2628-2646.

Chinese Quarterly Journal of Mathematics

2011年第2期

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The Conditions of Equivalence of a Class Germs of C~∞ Functions on Banach Spaces

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