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On equivalence of analytic functions to rational regular functions

Published online by Cambridge University Press:  09 April 2009

Wojciech Kucharz
Affiliation:
Department of MathematicsUniversity of New MexicoAlbuquerque, New Mexico 87131, U.S.A.
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Abstract

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We give sufficient conditions for an analytic function from Rn to R to be analytically equivalent to a rational regular function.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Bochnak, J., Kucharz, W. and Shiota, M., ‘On equivalence of ideals of real global analytic functions and the 17th Hilbert problem’, Invent. Math. 63 (1981), 403421.CrossRefGoogle Scholar
[2]Bochnak, J., Kucharz, W., and Shiota, M., ‘On algebraicity of global real analytic sets and functions’, Invent. Math. 70 (1982), 115156.CrossRefGoogle Scholar
[3]Lojasiewicz, S., Ensembles semi-analytiques (I.H.E.S., Lecture notes 1965).Google Scholar
[4]Shiota, M., ‘Equivalence of differentiable mappings and analytic mappings’, Inst. Hautes Etudes Sci. Publ. Math. 54 (1981), 37122.CrossRefGoogle Scholar
[5]Shiota, M., ‘Equivalence of differentiable functions, rational functions and polynomials’, Ann. Inst. Fourier (Grenoble) 32 (1982), 167204.CrossRefGoogle Scholar
[6]Thom, R., ‘L'équivalence d'une fonction différentiable et d'un polynôme’, Topology 3, Suppl. 2 (1965), 297307.CrossRefGoogle Scholar
[7]Tougeron, J. Cl., Idéaux de fonctions différentiables, (Springer, Berlin-Heidelberg-New York, 1972).CrossRefGoogle Scholar