Approximation polynomiale et extension holomorphe avec croissance sur une variété algébrique

• Autorzy: A. Zeriahi
• Języki publikacji: 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.

Słowa kluczowe

EN

Green function; L² estimation; approximation; growth; extension

Kategorie tematyczne

• 32A22: Nevanlinna theory (local); growth estimates; other inequalities
• 32D15: Continuation of analytic objects
• 32A15: Entire functions
• 32E30: Holomorphic and polynomial approximation, Runge pairs, interpolation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996
• Tom: 63
• Numer: 1
• Strony: 35-50

Daty

wydano

1996

otrzymano

1994-06-07

Twórcy

autor

A. Zeriahi

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

Bibliografia

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