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Preprints, Working Papers, ... Year : 2016

A QUANTITATIVE INTERPRETATION OF THE FREQUENT HYPERCYCLICITY CRITERION

Abstract

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.
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Dates and versions

hal-01395490 , version 1 (10-11-2016)
hal-01395490 , version 2 (17-11-2016)

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Romuald Ernst, A Mouze. A QUANTITATIVE INTERPRETATION OF THE FREQUENT HYPERCYCLICITY CRITERION. 2016. ⟨hal-01395490v2⟩

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