A QUANTITATIVE INTERPRETATION OF THE ...
Document type :
Pré-publication ou Document de travail
DOI :
Title :
A QUANTITATIVE INTERPRETATION OF THE FREQUENT HYPERCYCLICITY CRITERION
Author(s) :
Ernst, Romuald [Auteur]
Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville [LMPA]
Mouze, A [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Centrale Lille
Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville [LMPA]
Mouze, A [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Centrale Lille
English keyword(s) :
Frequent Hypercyclicity Criterion
Weighted densities
Weighted densities
HAL domain(s) :
Mathématiques [math]/Analyse fonctionnelle [math.FA]
English abstract : [en]
We give a quantitative interpretation of the Frequent Hypercyclicity Criterion. Actually we show that an operator which satisfies the Frequent Hypercyclicity Criterion is necessarily A-frequently hypercyclic, where A refers ...
Show more >We give a quantitative interpretation of the Frequent Hypercyclicity Criterion. Actually we show that an operator which satisfies the Frequent Hypercyclicity Criterion is necessarily A-frequently hypercyclic, where A refers to some weighted densities sharper than the natural lower density. In that order, we exhibit different scales of weighted densities that are of interest to quantify the " frequency " measured by the Frequent Hypercyclicity Criterion. Moreover we construct an example of unilateral weighted shift which is frequently hypercyclic but not A-frequently hypercyclic on a particular scale.Show less >
Show more >We give a quantitative interpretation of the Frequent Hypercyclicity Criterion. Actually we show that an operator which satisfies the Frequent Hypercyclicity Criterion is necessarily A-frequently hypercyclic, where A refers to some weighted densities sharper than the natural lower density. In that order, we exhibit different scales of weighted densities that are of interest to quantify the " frequency " measured by the Frequent Hypercyclicity Criterion. Moreover we construct an example of unilateral weighted shift which is frequently hypercyclic but not A-frequently hypercyclic on a particular scale.Show less >
Language :
Anglais
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