IJPAM: Volume 22, No. 1 (2005)

AN INTERPOLATION PROBLEM FOR PSEUDOCONVEX
DOMAINS OF CERTAIN INFINITE-DIMENSIONAL
COMPLEX VECTOR SPACES

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Let $U$ be a pseudoconvex domain of an infinite-dimensional complex vector space equipped with the finite topology. Here we show the surjectivity of the restriction map $H^0(U,\mathcal {O}_U) \to H^0(Z,\mathcal {O}_Z)$ for certain ``zero-dimensional'' closed subschemes of $U$ (e.g. we may take as $Z$ any countable discrete subset of $U$). Due to the chosen topology of $V$ this is essentially an interpolation problem for Gâteaux analytic functions.

Received: April 12, 2005

AMS Subject Classification: 32K05

Key Words and Phrases: pseudoconvex domains, interpolation, pseudoconvexity in infinite-dimensional vector spaces, Gâteaux analitic function

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 22
Issue: 1