The differentiation operator in the space of uniformly convergent Dirichlet series

Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fréchet space of all Dirichlet series that are uniformly convergent in all half‐planes {s∈C|Res>ε} for each ε>0. The properties of the formal inverse of the differ...

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Bibliographic Details
Published in:Mathematische Nachrichten 2020-08, Vol.293 (8), p.1452-1458
Main Author: Bonet, José
Format: Article
Language:English
Subjects:
abscissas of convergence
Convergence
Differentiation
differentiation operator
Dirichlet problem
Fréchet space
integration operator
spaces of Dirichlet series
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Summary:Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fréchet space of all Dirichlet series that are uniformly convergent in all half‐planes {s∈C|Res>ε} for each ε>0. The properties of the formal inverse of the differentiation are also investigated.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201900211