Recent trends in harmonic and complex analysis

Density of translates in weighted Lp spaces on locally compact groups

3 avr. 2017, 17:30

45m

Salle de séminaire (Université d'Orléans, Mathématiques)

Orateur

Dr Yulia Kuznetsova (Université de Bourgogne Franche Comté)

Description

Let $G$ be a locally compact group, and let $1\le p<\mathrm{\infty }$. Consider the weighted $L^p$-space $L^p(G,\omega )=\{f:\int |f\omega {|}^p<\mathrm{\infty }\}$, where $\text{Undefined control sequence R}$ 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 $\text{Undefined control sequence Z}$ . 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).