一类实奇芽等价的充要条件(英文)

The Necessary and Sufficient Conditions of Equivalence of a Class of Real Singular Germs 

英文关键词:converse theorem  Fredholm germ  implicit function.

中文摘要:

      给定一自反的Ｂａｎａｃｈ空间Ｘ．在ｃ^∞函数芽环∈（Ｘ）中，任何在原点Ｏ∈Ｘ的实奇芽ｆ，若其二阶Ｆｒｅｃｈｅｔ导数ｆ″（０）＝Ｔ是一个Ｆｒｅｄｈｏｌｍ算子，则它同构于形如：1/2+g(v)的一个芽．如果代替ｇ以一个与之同构的芽ｇ_１，显然得到一个与原来的芽同构的芽．然而，其逆是否真呢？本文将证明其逆命题亦真

英文摘要:

      Given a reflexive Banach space X .In the ring of C^∞ function germ s∈(X) ,any real singular germ f in ∈(X) whose second Frechet derivative at origin f″(0)=T is a Fredholm operator is isomorphic to a germ of the form 1/2+g(v) .If we replace g by a g_１ which is isomorphic to g ,we clearly obtain a germ in ∈(X) which is isomorphic to the original one. However,is true converse of this proposition?In this paper,we will show that the converse is also true.