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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Topologically principal part of analytic functions
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by Etsuo Yoshinaga PDF
Trans. Amer. Math. Soc. 314 (1989), 803-814 Request permission

Abstract:

The problem of ${C^0}$-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).
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 314 (1989), 803-814
  • MSC: Primary 58C27
  • DOI: https://doi.org/10.1090/S0002-9947-1989-0930085-5
  • MathSciNet review: 930085