Growth of frequently hypercyclic functions for some weighted Taylor shifts on the unit disc

Mouze, Augustin; Munnier, Vincent

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.4153/S0008439520000430

Title :

Growth of frequently hypercyclic functions for some weighted Taylor shifts on the unit disc

Author(s) :

Mouze, Augustin [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Centrale Lille
Munnier, Vincent [Auteur]

Journal title :

Canadian Mathematical Bulletin

Pages :

264-281

Publisher :

Cambridge University Press

Publication date :

2021

ISSN :

0008-4395

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

Abstract For any $\alpha \in \mathbb {R},$ we consider the weighted Taylor shift operators $T_{\alpha }$ acting on the space of analytic functions in the unit disc given by $T_{\alpha }:H(\mathbb {D})\rightarrow H(\mathbb ...
Show more >Abstract For any $\alpha \in \mathbb {R},$ we consider the weighted Taylor shift operators $T_{\alpha }$ acting on the space of analytic functions in the unit disc given by $T_{\alpha }:H(\mathbb {D})\rightarrow H(\mathbb {D}),$ $$ \begin{align*}f(z)=\sum_{k\geq 0}a_{k}z^{k}\mapsto T_{\alpha}(f)(z)=a_1+\sum_{k\geq 1}\Big(1+\frac{1}{k}\Big)^{\alpha}a_{k+1}z^{k}.\end{align*}$$ We establish the optimal growth of frequently hypercyclic functions for $T_\alpha $ in terms of $L^p$ averages, $1\leq p\leq +\infty $ . This allows us to highlight a critical exponent.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

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