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The Fréchet Schwartz Algebra of Uniformly Convergent Dirichlet Series

Part of: Holomorphic functions of several complex variables Series expansions Special classes of linear operators Topological linear spaces and related structures

Published online by Cambridge University Press:  07 May 2018

José Bonet
José Bonet*
Affiliation:
Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politècnica de València, E-46071 Valencia, Spain ([email protected])
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Abstract

The algebra of all Dirichlet series that are uniformly convergent in the half-plane of complex numbers with positive real part is investigated. When it is endowed with its natural locally convex topology, it is a non-nuclear Fréchet Schwartz space with basis. Moreover, it is a locally multiplicative algebra but not a Q-algebra. Composition operators on this space are also studied.

Keywords

Dirichlet seriesabscissas of convergenceFréchet spacescomposition operatorstopological algebras

MSC classification

Primary: 46A04: Locally convex Fréchet spaces and (DF)-spaces
Secondary: 30B50: Dirichlet series and other series expansions, exponential series 32A05: Power series, series of functions 46A03: General theory of locally convex spaces 46A11: Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) 46A45: Sequence spaces (including Köthe sequence spaces) 47B33: Composition operators
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 4 , November 2018 , pp. 933 - 942
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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