We study universal holomorphic functions on a Stein manifold M with projective compactification. Let {φ_n} be a sequence of holomorphic automorphisms of M. We pove that if {φ_n^-1} is A run-away, then the set of all universal functions with respect to {φ_n} in A(K) for all compact subsets K with a certain propoerty is the intersection of contable number of open dense subsets in the space of all holomorphic functions on M. We also note that there is a close connection between the direction of run-awayness and a family of compact sets for which there exists a universal function.

Universal functions on Stein manifolds

ZAPPA, Paolo
2004

Abstract

We study universal holomorphic functions on a Stein manifold M with projective compactification. Let {φ_n} be a sequence of holomorphic automorphisms of M. We pove that if {φ_n^-1} is A run-away, then the set of all universal functions with respect to {φ_n} in A(K) for all compact subsets K with a certain propoerty is the intersection of contable number of open dense subsets in the space of all holomorphic functions on M. We also note that there is a close connection between the direction of run-awayness and a family of compact sets for which there exists a universal function.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11391/42728
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