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Approximation polynomiale et extension holomorphe avec croissance sur une variété algébrique

100%

Zeriahi A.

Annales Polonici Mathematici

1996

tom 63

nr 1

35-50

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.

Une nouvelle version du théorème d'extension de Hartogs pour les applications séparément holomorphes entre espaces analytiques

63%

Alehyane O., Zeriahi A.

Annales Polonici Mathematici

2001

tom 76

nr 3

245-278

This paper is concerned with the problem of extension of separately holomorphic mappings defined on a "generalized cross" of a product of complex analytic spaces with values in a complex analytic space. The crosses considered here are inscribed in Borel rectangles (of a product of two complex analytic spaces) which are not necessarily open but are non-pluripolar and can be quite small from the topological point of view. Our first main result says that the singular set of a given separately holomorphic mapping defined on such a cross is quite small from the pluripotential point of view in the product space in the sense that each of its projections is pluripolar. Then for some special crosses, we deduce more precise results on the extension of separately holomorphic mappings on such crosses, giving generalizations of all the main results obtained earlier by various authors in this direction.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Zeriahi A.

1 Alehyane O.

1 2001

1 1996

Wyniki wyszukiwania

Approximation polynomiale et extension holomorphe avec croissance sur une variété algébrique

Une nouvelle version du théorème d'extension de Hartogs pour les applications séparément holomorphes entre espaces analytiques