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Frequently hypercyclic random vectors

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 09 Dec 2022Embargo end date: 01 Jan 2022 Belgium English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society, volume 151, pages 1,103-1,117 (issn: 0002-9939, eissn: 1088-6826, Copyright policy )
Authors: Agneessens, Kevin;

doi: 10.1090/proc/16153 , 10.48550/arxiv.2204.10091

arXiv: 2204.10091

handle: 20.500.12907/44480

Frequently hypercyclic random vectors

Abstract

We show that, under suitable conditions, an operator acting like a shift on some sequence space has a frequently hypercyclic random vector whose distribution is strongly mixing for the operator. This result will be applied to chaotic weighted shifts. We also apply it to every operator satisfying the Frequent Hypercyclicity Criterion, recovering a result of Murillo and Peris.

Country
Belgium
Related Organizations
Keywords

ergodic theory, frequently hypercyclic operators, Applied Mathematics, General Mathematics, Physique, chimie, mathématiques & sciences de la terre, Cyclic vectors, hypercyclic and chaotic operators, weighted shifts, Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.), Functional Analysis (math.FA), Mathematics - Functional Analysis, Mathématiques, Physical, chemical, mathematical & earth Sciences, Linear operators on function spaces (general), FOS: Mathematics, 47A16, 47A35, 47B37, 47B38, Mathematics, Ergodic theory of linear operators

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    popularity
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    		 Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Top 10%
Average
Average
Green