ZARRABI, Mohamed

doi:10.1016/j.jmaa.2012.07.024

Métadonnées

Afficher la notice complète

Licence d’utilisation du document

ZARRABI, Mohamed
Institut de Mathématiques de Bordeaux [IMB]

Langue

Article de revue

Ce document a été publié dans

Journal of Mathematical Analysis and Applications. 2013, vol. 397, n° 1, p. 109-118

Elsevier

Résumé en anglais

For semigroups $S=\R_+, \ \Z_+$ and $\Z_+^k$, we show that if $T$ is a representation of $S$ by contractions on a {\it Hilbert space} then \\ $\inf_{t\in S}\Vert T(t)\widehat f (T)\Vert=\sup\left\{|f(\lambda)|,\ \lambda\in \textrm{Sp}_u (T,S)\right\}$, where $f\in L^1(S)$ and $\text{Sp}_u (T,S)$ is the unitary spectrum of $T$ with respect to $S$. When $T$ is a representation of a suitable semigroup $S$ by contractions on a {\it Banach space}, we give sharp conditions on $\textrm{Sp}_u (T,S)$ which guarantee that the equality above holds. These conditions concern the thinness of $\textrm{Sp}_u (T,S)$ in the harmonic analysis sense. These results are related to theorems of Katzelson-Tzafriri type, which give conditions guaranteeing that $\inf_{t\in S}\Vert T(t)\widehat f (T)\Vert$ vanishes.< Réduire

Mots clés en anglais

Representations

Locally compact abelian group

semigroup

contractions

spectral synthesis

Helson set.

Helson set

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189378

DOI

http://dx.doi.org/10.1016/j.jmaa.2012.07.024

Project ANR

/ - ANR-09-BLAN-0058

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251