Journal of the Mathematical Society of Japan

Universal functions on Stein manifolds

Yukitaka ABE and Paolo ZAPPA

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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.

Article information

J. Math. Soc. Japan, Volume 56, Number 1 (2004), 31-43.

First available in Project Euclid: 3 October 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32A17: Special families of functions
Secondary: 32Q28: Stein manifolds

Universal functions Stein manifolds automorphisms A run-away sequences


ABE, Yukitaka; ZAPPA, Paolo. Universal functions on Stein manifolds. J. Math. Soc. Japan 56 (2004), no. 1, 31--43. doi:10.2969/jmsj/1191418694.

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