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1996 | 63 | 1 | 35-50

Tytuł artykułu

Approximation polynomiale et extension holomorphe avec croissance sur une variété algébrique

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Treść / Zawartość

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FR

Abstrakty

EN
We first give a general growth version of the theorem of Bernstein-Walsh-Siciak concerning the rate of convergence of the best polynomial approximation of holomorphic functions on a polynomially convex compact subset of an affine algebraic manifold. This can be considered as a quantitative version of the well known approximation theorem of Oka-Weil. Then we give two applications of this theorem. The first one is a generalization to several variables of Winiarski's theorem relating the growth of an entire function to the rate of convergence of its best polynomial approximation; the second application concerns the extension with growth of an entire function from an algebraic submanifold to the whole space.

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Twórcy

autor
  • Laboratoire d'Analyse, Université Paul Sabatier, 118, Route de Narbonne, 31062 Toulouse Cedex, France

Bibliografia

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