TOPOLOGICALLY PRINCIPAL PART OF ANALYTIC FUNCTIONS
TOPOLOGICALLY PRINCIPAL PART OF ANALYTIC FUNCTIONS
复制标题
解析函数的拓扑主要部分
DOI：
10.1090/s0002-9947-1989-0930085-5
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发表时间：
1989
影响因子：
1.3
通讯作者：
Etsuo Yoshinaga
中科院分区：
文献类型：
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作者：
Etsuo Yoshinaga
射流的co -充分性问题是函数或奇点理论中最有趣的问题之一。粗略地说，它是确定给定函数f(x)在欧几里德空间原点泰勒展开的拓扑主部的问题。在这里，拓扑主部分应该满足这样的性质：它是f(x)的泰勒展开式中尽可能小的一部分，并且f(x)在原点处的局部拓扑类型由它决定。如果函数f(x)在原点是孤立的奇点，或者具有非简并的牛顿主部（见（1.2）），那么我们就知道这个问题的一些答案（见（1.1），（1.3））。本文的目的是对任意解析函数给出这一问题的一些结果。主要结果见式（1.5）、（1.6）和（1.7）。1. 主要结果
The problem of CO-sufficiency of jets is one of the most interesting problems in the theory of functions or singularities. Roughly speaking, it is the problem of determining a topologically principal part of the Taylor expansion of a given function f(x) at the origin of Euclidean space. Here, the topologically principal part should satisfy the properties that it is as small as possible a part of the Taylor expansion of f(x) and that the local topological type of f(x) at the origin is determined by it. If a function f(x) is an isolated singularity at the origin or has a nondegenerate Newton principal part (see (1.2)), then we know some answers to this problem (see (1.1), (1.3)). The purpose of this paper is to give some results for this problem for any analytic function. The main results are formulated in (1.5), (1.6), and (1.7). 1. MAIN RESULTS