ArticleOriginal scientific text

Title

Equivalence of analytic and rational functions

Authors 1, 2, 2

Affiliations

  1. Department of Mathematics, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
  2. Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, U.S.A.

Abstract

We give a criterion for a real-analytic function defined on a compact nonsingular real algebraic set to be analytically equivalent to a rational function.

Keywords

analytic function, rational function, analytic equivalence

Bibliography

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  2. J. Bochnak, W. Kucharz and M. Shiota, On algebraicity of global real analytic sets and functions, Invent. Math. 70 (1982), 115-156.
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  4. M. Shiota, Equivalence of differentiable mappings and analytic mappings, Inst. Hautes Études Sci. Publ. Math. 54 (1981), 237-322.
  5. M. Shiota, Equivalence of differentiable functions, rational functions and polynomials, Ann. Inst. Fourier (Grenoble) 32 (1982), 167-204.
  6. R. Thom, L'équivalence d'une fonction différentiable et d'un polynôme, Topology 3 (1965), suppl. 2, 297-307.
  7. J. C. Tougeron, Idéaux de fonctions différentiables, Ergeb. Math. Grenzgeb. 71, Springer, 1972.
Pages:
37-42
Main language of publication
English
Received
1995-06-20
Published
1997
Exact and natural sciences