Multiply universal holomorphic functions
type: Item
instance of: scholarly article
title: Multiply universal holomorphic functions
zbMATH Open document ID: 0874.30029
author: W. Luh
published in: Journal of Approximation Theory
publication date: 1997-06-10T00:00:00Z
review text: The problem of the existence of so-called ``universal functions'' (compare W. Luh, Holomorphic monsters. [J. Approximation Theory 53, No. 2, 128-144 (1988; Zbl 0669.30020)] for the notations and the history of the topic) is generalized. The main result is the following: Let \({\mathcal O} \subset\mathbb{C}\), \({\mathcal O} \neq\mathbb{C}\), be an open set with simply connected components. Then there exists a function \(\varphi\), which is holomorphic exactly on \({\mathcal O}\) and has six universal properties at the same time. The proof uses essentially the theorems of Runge and Mergelyan.
Mathematics Subject Classification ID: 30E10
zbMATH DE Number: 1019187
reviewed by: Rolf Wallisser
MaRDI profile type: Publication
full work available at URL: jath.1997.3036
OpenAlex ID: W1973969195
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DOI: 10.1006/JATH.1997.3036
description: scientific article; zbMATH DE number 1019187