Functiones et Approximatio Commentarii Mathematici
- Funct. Approx. Comment. Math.
- Volume 59, Number 2 (2018), 285-304.
Dirichlet series from the infinite dimensional point of view
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.
Funct. Approx. Comment. Math., Volume 59, Number 2 (2018), 285-304.
First available in Project Euclid: 26 June 2018
Permanent link to this document
Digital Object Identifier
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]
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. https://projecteuclid.org/euclid.facm/1529978435