## Journal of the Mathematical Society of Japan

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

### Universal functions on Stein manifolds

#### Abstract

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

**Permanent link to this document**

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

**Keywords**

Universal functions Stein manifolds automorphisms A run-away sequences

#### 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