Frequent hypercyclicity of random holomorphic functions for Taylor shifts and optimal growth

We give a probabilistic construction of frequently hypercyclic holomorphic functions for the Taylor shifts. In particular this method allows us to strengthen a recent result regarding the frequent hypercyclicity of such operators. Moreover we obtain optimal growth of the frequently hypercyclic funct...

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Bibliographic Details
Published inJournal d'analyse mathématique (Jerusalem) Vol. 143; no. 2; pp. 615 - 637
Main Authors Mouze, Augustin, Munnier, Vincent
Format Journal Article
LanguageEnglish
Published Jerusalem The Hebrew University Magnes Press 01.06.2021
Springer Nature B.V
Springer
Subjects
Abstract Harmonic Analysis
Analysis
Analytic functions
Dynamical Systems and Ergodic Theory
Functional Analysis
Mathematical analysis
Mathematics
Mathematics and Statistics
Partial Differential Equations
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Summary:We give a probabilistic construction of frequently hypercyclic holomorphic functions for the Taylor shifts. In particular this method allows us to strengthen a recent result regarding the frequent hypercyclicity of such operators. Moreover we obtain optimal growth of the frequently hypercyclic functions with respect to the Taylor shift acting on H (ⅅ).
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-021-0164-5