## Journal of the Mathematical Society of Japan

### Universal functions on Stein manifolds

#### Abstract

We study universal holomorphic functions on a Stein manifold $M$ with projective compactification. Let $\{\varphi_{n}\}$ be a sequence of holomorphic automorphisms of $M$. We prove that if $\{\varphi_{n}^{-1}\}$ is $A$ run-away, then the set of all universal functions with respect to $\{\varphi_{n}\}$ in $\mathscr{A}(K)$ 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

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

Dates
First available in Project Euclid: 3 October 2007

https://projecteuclid.org/euclid.jmsj/1191418694

Digital Object Identifier
doi:10.2969/jmsj/1191418694

Mathematical Reviews number (MathSciNet)
MR2023452

Zentralblatt MATH identifier
1052.32005

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

#### Citation

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