arXiv subjects
Publications and source records attributed to Vagia Vlachou.
In this article, we study disjoint universality for certain sequences of operators, that are connected with the differential operator. Actually, the motivation to study such sequences comes from Universal Taylor series, if you change the role of the center of convergence.
A holomorphic function f on a simply connected domain $Ω$ belongs to a subclass of universal Taylor series if prescribed and infinite number of partial sums of the Taylor expansion of f around a given center $ζ_0$ realize Mergalyan-type approximations outside $Ω$. We will prove that this class is independent of the choice of center if the indices of the partial sums do not grow very fast to infinity.
We give necessary and sufficient condition so that we have d-hypercyclicity for operators who map a holomorphic function to a partial sum of the Taylor expansion. This problem is connected with doubly universal Taylors series and this is an effort to generalize the concept to multiple universal Taylor series.
We show that families of translation operators, where the translates grow exponentially fast, do not admit common hypercyclic functions. The result is close to be optimal.