Some results of Katznelson-Tzafriri type
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ZARRABI, Mohamed | |
| dc.date.accessioned | 2024-04-04T02:19:10Z | |
| dc.date.available | 2024-04-04T02:19:10Z | |
| dc.date.created | 2009-03-05 | |
| dc.date.issued | 2013 | |
| dc.identifier.issn | 0022-247X | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189378 | |
| dc.description.abstractEn | 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. | |
| dc.description.sponsorship | / - ANR-09-BLAN-0058 | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | Representations | |
| dc.subject.en | Locally compact abelian group | |
| dc.subject.en | semigroup | |
| dc.subject.en | contractions | |
| dc.subject.en | spectral synthesis | |
| dc.subject.en | Helson set. | |
| dc.subject.en | Helson set | |
| dc.title.en | Some results of Katznelson-Tzafriri type | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.jmaa.2012.07.024 | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| bordeaux.journal | Journal of Mathematical Analysis and Applications | |
| bordeaux.page | 109-118 | |
| bordeaux.volume | 397 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00461677 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00461677v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Mathematical%20Analysis%20and%20Applications&rft.date=2013&rft.volume=397&rft.issue=1&rft.spage=109-118&rft.epage=109-118&rft.eissn=0022-247X&rft.issn=0022-247X&rft.au=ZARRABI,%20Mohamed&rft.genre=article |
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