A QUANTITATIVE INTERPRETATION OF THE FREQUENT HYPERCYCLICITY CRITERION
Résumé
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.
Domaines
Analyse fonctionnelle [math.FA]
Origine : Fichiers produits par l'(les) auteur(s)
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