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On equivalence of analytic functions to rational regular functions

  • Wojciech Kucharz (a1)

Abstract

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

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References

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

  • Wojciech Kucharz (a1)

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