On a universality property of certain integral operators (Q1588423)

If \(X\), \(Y\) are topological vector spaces, \(S_n:X\to Y\) is a continuous linear mapping for every \(n\in\mathbb{N}\) and \[ U:= \{x\in X;\;\overline{\{S_n x;n\in\mathbb{N}\}}= Y\}, \] then every \(x\in U\) is hypercyclic (universal) for \(\{S_n\}_{n\in\mathbb{N}}\). \(U\) is a residual class of \(X\) if the set \(X\setminus U\) is of first category in \(X\). \textit{G. Herzog} [Math. Nachr. 188, 169-171 (1997; Zbl 0886.35026)] has recently proved such a universality property for an integral operator associated to solutions of the initial value problem for the heat equation. In this paper, the authors extend the result of G. Herzog to Fourier and Hankel convolution operators and Dunkl transforms.