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INEGALITES DE MARKOV SINGULIERES ET APPROXIMATION DES FONCTIONS HOLOMORPHES DE LA CLASSE M

Abstract : In the first part, we prove that all the singular algebraic curves of Rn admit Markov tangential inequalities. We give a geometric signification of the Markov exponent. We prove that this exponent is less or equal to the multiplicity of the singularity of the complexify curve in Cn . We construct a Puiseux parameterisation on the real singularity and we extended it to a nowhere dense open subset of C. Therefore, we obtain the property HCP of the Green function with pole at infinity by geodesic metric in the complexify curve. In the second part, we prove a Bernstein type theorem for the functions of intermediate classes between holomorphic functions and C¥ functions on subclasses of s-H convex compact subsets of Cn. To prove this result, we give representative kernel on s-H convex compact for functions of A¥(K). We approach this kernel by an other kernel type Henkin-Ramirez. We propose a new geometric property of Green function with pole at infinity and we give some examples.
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https://tel.archives-ouvertes.fr/tel-00010810
Contributor : Laurent Gendre <>
Submitted on : Friday, October 28, 2005 - 2:51:26 PM
Last modification on : Friday, January 10, 2020 - 9:08:06 PM
Long-term archiving on: : Friday, November 25, 2016 - 9:48:12 AM

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  • HAL Id : tel-00010810, version 3

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Laurent Gendre. INEGALITES DE MARKOV SINGULIERES ET APPROXIMATION DES FONCTIONS HOLOMORPHES DE LA CLASSE M. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2005. Français. ⟨tel-00010810v3⟩

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