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Approximation of Holomorphic Solutions of a System of Real Analytic Equations

Published online by Cambridge University Press:  20 November 2018

M. Hickel  and
G. Rond
M. Hickel
Affiliation:
Université Bordeaux 1, I.M.B., Equipe d’Analyse et Géométrie, et I.U.T. Bordeaux 1 département Informatique, 33405 Talence Cedex, Francee-mail: hickel@math.u-bordeaux1.fr
G. Rond
Affiliation:
I.M.L. Faculté des Sciences de Luminy, Case 907, 163 av. de Luminy, 13288 Marseille Cedex 9, Francee-mail: rond@iml.univ-mrs.fr
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Abstract

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We prove the existence of an approximation function for holomorphic solutions of a system of real analytic equations. For this we use ultraproducts andWeierstrass systems introduced by J. Denef and L. Lipshitz. We also prove a version of the Płoski smoothing theorem in this case.

Keywords

13B4013L0514F12Artin approximationreal analytic equations
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 4 , 01 December 2012 , pp. 752 - 761
Copyright
Copyright © Canadian Mathematical Society 2012

References

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