### Speaker

Dr
Yulia Kuznetsova
(Université de Bourgogne Franche Comté)

### Description

Let $G$ be a locally compact group, and let $1\le p < \infty$. Consider the weighted $L^p$-space
$L^p(G,\omega)=\{f:\int|f\omega|^p<\infty\}$, where $\omega:G\to \R$ is a
positive measurable function. Under appropriate conditions on $\omega$, $G$ acts on $L^p(G,\omega)$
by translations. When is this action hypercyclic, that is, there is a function in this space such that
the set of all its translations is dense in $L^p(G,\omega)$? H.Salas (1995) gave a criterion of
hypercyclicity in the case $G=\Z$ . Under mild assumptions, we present a corresponding
characterization for a general locally compact group $G$. Our results are obtained in a more general
setting when the translations only by a subset $S\subset G$ are considered.
Joint work with E. Abakumov (Paris-Est).