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...
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...
In our earlier paper [CKZ], we proved that any plurisubharmonic function on a bounded hyperconvex domain in with zero boundary values in a quite general sense, admits a plurisubharmonic subextension to a larger hyperconvex domain. Here we study important properties of its maximal subextension and give informations on its Monge-Ampère measure. More generally, given a quasi-plurisubharmonic function on a given quasi-hyperconvex domain of a compact Kähler manifold , with well defined Monge-Ampère...
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