Costakis, G., Tsirivas, N. and Vlachou, V. (2015) Non-Existence of Common Hypercyclic Vectors for Certain Families of Translation Operators. Computational Methods and Function Theory, 15, 393-401.
https://doi.org/10.1007/s40315-015-0107-1

has been cited by the following article:

• TITLE: Uniform Convergence of Translation Operators

  AUTHORS: Nikolaos Tsirivas

  KEYWORDS: Hypercyclic Operator, Common Hypercyclic Vectors, Translation Operator

  JOURNAL NAME: Advances in Pure Mathematics, Vol.12 No.12, December 12, 2022

  ABSTRACT: We denote N, R, Cthe sets of natural, real and complex numbers respectively. Let (λn), n ∈ N be an unbounded sequence of complex numbers. Costakis has proved the following result. There exists an entire function f with the following property: for every x, y ∈ R with 0 , every θ ∈(0,1) and every a ∈ C there is a subsequence of natural numbers (mn), n ∈ N such that, for every compact subset L ⊆ C , In the present paper we show that the constant function a cannot be replaced by any non-constant entire function G. This is so even if one demands the convergence in (*) only for a single radius r and a single positive number θ. This result is related with the problem of existence of common universal vectors for an uncountable family of sequences of translation operators.