A QUANTITATIVE INTERPRETATION OF THE FREQUENT HYPERCYCLICITY CRITERION

Ernst, Romuald; Mouze, A

Document type :

Pré-publication ou Document de travail

DOI :

10.1017/etds.2017.55

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

English keyword(s) :

Frequent Hypercyclicity Criterion
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 >

Language :

Anglais

ANR Project :

Frontières de la théorie des opérateurs

Collections :