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December 2018 Dirichlet series from the infinite dimensional point of view
Andreas Defant, Domingo García, Manuel Maestre, Pablo Sevilla-Peris
Funct. Approx. Comment. Math. 59(2): 285-304 (December 2018). DOI: 10.7169/facm/1741

Abstract

A classical result of Harald Bohr linked the study of convergent and bounded Dirichlet series on the right half plane with bounded holomorphic functions on the open unit ball of the space $c_0$ of complex null sequences. Our aim here is to show that many questions in Dirichlet series have very natural solutions when, following Bohr's idea, we translate these to the infinite dimensional setting. Some are new proofs and other new results obtained by using that point of view.

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Andreas Defant. Domingo García. Manuel Maestre. Pablo Sevilla-Peris. "Dirichlet series from the infinite dimensional point of view." Funct. Approx. Comment. Math. 59 (2) 285 - 304, December 2018. https://doi.org/10.7169/facm/1741

Information

Published: December 2018
First available in Project Euclid: 26 June 2018

zbMATH: 07055557
MathSciNet: MR3892307
Digital Object Identifier: 10.7169/facm/1741

Subjects:
Primary: 30B50
Secondary: 46G20

Keywords: Banach space , Bohr transform , Dirichlet series , holomorphic function

Rights: Copyright © 2018 Adam Mickiewicz University

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Vol.59 • No. 2 • December 2018
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