WEIGHTED HOLOMORPHIC DIRICHLET SERIES AND COMPOSITION OPERATORS WITH POLYNOMIAL SYMBOLS

Mau, Camille; Fricain, Emmanuel

Document type :

Compte-rendu et recension critique d'ouvrage

Title :

WEIGHTED HOLOMORPHIC DIRICHLET SERIES AND COMPOSITION OPERATORS WITH POLYNOMIAL SYMBOLS

Author(s) :

Mau, Camille [Auteur]
Nanayang Technological University [NTU]
Fricain, Emmanuel [Auteur]

Université de Lille
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Mathematica Scandinavica

Pages :

109--146

Publication date :

2022

English keyword(s) :

Weighted holomorphic Dirichlet series
composition operator
cyclicity

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

In this paper, we introduce a general class of weighted spaces of holomorphic Dirichlet series (with real frequencies) analytic in some half-plane and study composition operators on these spaces. In the particular case ...
Show more >In this paper, we introduce a general class of weighted spaces of holomorphic Dirichlet series (with real frequencies) analytic in some half-plane and study composition operators on these spaces. In the particular case when the symbol inducing the composition operator is an affine function, we give criteria for boundedness and compactness. We also study the cyclicity property and as a byproduct give a characterization so that the direct sum of the identity plus a weighted forward shift operator on $\ell^2$ is cyclic. ContentsShow less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :