A quantitative interpretation of the frequent hypercyclicity criterion

Ernst, Romuald; Mouze, Augustin

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1017/etds.2017.55

Title :

A quantitative interpretation of the frequent hypercyclicity criterion

Author(s) :

Ernst, Romuald [Auteur]
Mouze, Augustin [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Centrale Lille

Journal title :

Ergodic Theory and Dynamical Systems

Pages :

898-924

Publisher :

Cambridge University Press (CUP)

Publication date :

2019

ISSN :

0143-3857

HAL domain(s) :

Mathématiques [math]

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 $A$ ...
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 a unilateral weighted shift which is frequently hypercyclic but not $A$ -frequently hypercyclic on a particular scale.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Frontières de la théorie des opérateurs

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Files

1611.04368
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