Reference : Common Universal Meromorphic Functions for Translation and Dilation Mappings
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Common Universal Meromorphic Functions for Translation and Dilation Mappings
Meyrath, Thierry mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)]
In press
Computational Methods and Function Theory
Yes (verified by ORBilu)
[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

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