Reference : Common Universal Meromorphic Functions for Translation and Dilation Mappings
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/49684
Common Universal Meromorphic Functions for Translation and Dilation Mappings
English
Meyrath, Thierry mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]
In press
Computational Methods and Function Theory
Springer
Yes
International
1617-9447
2195-3724
Germany
[en] Universality ; Hypercyclicity ; Meromorphic functions ; Runge's Theorem ; Ansari's Theorem
[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.
http://hdl.handle.net/10993/49684
10.1007/s40315-021-00429-x
https://link.springer.com/article/10.1007/s40315-021-00429-x

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