The Ces\`{a}ro space of Dirichlet series and its multiplier algebra
Jorge Bueno-Contreras, Guillermo P. Curbera, Olvido Delgado

TL;DR
This paper studies a Banach space of Dirichlet series with coefficients in Cesàro sequence spaces, analyzing its domain of analyticity, point evaluation boundedness, and identifying its multiplier algebra as a Wiener algebra shifted to a half-plane.
Contribution
It characterizes the space of Dirichlet series with Cesàro sequence coefficients and identifies its multiplier algebra as a shifted Wiener algebra, extending understanding of these function spaces.
Findings
Maximal domain of analyticity determined
Boundedness of point evaluations analyzed
Multiplier algebra identified as shifted Wiener algebra
Abstract
We consider the space of all Dirichlet series whose coefficients belong to the Ces\`{a}ro sequence space , consisting of all complex sequences whose absolute Ces\`{a}ro means are in , for . It is a Banach space of analytic functions, for which we study the maximal domain of analyticity and the boundedness of point evaluations. We identify the algebra of analytic multipliers on as the Wiener algebra of Dirichlet series shifted to the vertical half-plane , where .
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Taxonomy
TopicsAdvanced Banach Space Theory · Advanced Topics in Algebra · Holomorphic and Operator Theory
