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The differentiation operator in the space of uniformly convergent Dirichlet series

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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… Click to show full abstract

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.

Keywords: differentiation; uniformly convergent; differentiation operator; dirichlet series; space

Journal Title: Mathematische Nachrichten
Year Published: 2020

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