Common Universal Meromorphic Functions for Translation and Dilation Mappings

Reference : Common Universal Meromorphic Functions for Translation and Dilation Mappings


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/49684

Title :	Common Universal Meromorphic Functions for Translation and Dilation Mappings
Language :	English
Author, co-author :	Meyrath, Thierry [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]
Publication date :	2022
Journal title :	Computational Methods and Function Theory
Publisher :	Springer
Volume :	22
Issue/season :	4
Pages :	781 - 798
Peer reviewed :	Yes
Audience :	International
ISSN :	1617-9447
e-ISSN :	2195-3724
Country :	Germany
Keywords :	[en] Universality ; Hypercyclicity ; Meromorphic functions ; Runge's Theorem ; Ansari's Theorem
Abstract :	[en] We consider translation and dilation mappings acting on the spaces of meromorphic functions on the complex plane and the punctured complex plane, respectively. In both cases, we show that there is a dense $G_{\delta}$-subset of meromorphic functions that are common universal for certain uncountable families of these mappings. While a corresponding result for translations exists for entire functions, our result for dilations has no holomorphic counterpart. We further obtain an analogue of Ansari’s Theorem for the mappings we consider, which is used as a key tool in the proofs of our main results.
Permalink :	http://hdl.handle.net/10993/49684
DOI :	10.1007/s40315-021-00429-x
Other URL :	https://link.springer.com/article/10.1007/s40315-021-00429-x

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