Functiones et Approximatio Commentarii Mathematici

Dirichlet series from the infinite dimensional point of view

Andreas Defant, Domingo García, Manuel Maestre, and Pablo Sevilla-Peris

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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.

Article information

Funct. Approx. Comment. Math., Volume 59, Number 2 (2018), 285-304.

First available in Project Euclid: 26 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30B50: Dirichlet series and other series expansions, exponential series [See also 11M41, 42-XX]
Secondary: 46G20: Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10]

Dirichlet series Bohr transform holomorphic function Banach space


Defant, Andreas; García, Domingo; Maestre, Manuel; Sevilla-Peris, Pablo. Dirichlet series from the infinite dimensional point of view. Funct. Approx. Comment. Math. 59 (2018), no. 2, 285--304. doi:10.7169/facm/1741.

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