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January, 2004 Universal functions on Stein manifolds
Yukitaka ABE, Paolo ZAPPA
J. Math. Soc. Japan 56(1): 31-43 (January, 2004). DOI: 10.2969/jmsj/1191418694


We study universal holomorphic functions on a Stein manifold M with projective compactification. Let {ϕn} be a sequence of holomorphic automorphisms of M. We prove that if {ϕn-1} is A run-away, then the set of all universal functions with respect to {ϕn} in A(K) for all compact subsets K with a certain property is the intersection of countable 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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Yukitaka ABE. Paolo ZAPPA. "Universal functions on Stein manifolds." J. Math. Soc. Japan 56 (1) 31 - 43, January, 2004.


Published: January, 2004
First available in Project Euclid: 3 October 2007

zbMATH: 1052.32005
MathSciNet: MR2023452
Digital Object Identifier: 10.2969/jmsj/1191418694

Primary: 32A17
Secondary: 32Q28

Keywords: A run-away sequences , automorphisms , Stein manifolds , Universal functions

Rights: Copyright © 2004 Mathematical Society of Japan


Vol.56 • No. 1 • January, 2004
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