Defant, Andreas; García, Domingo; Maestre, Manuel; Sevilla Peris, Pablo(Adam Mickiewicz University The Faculty of Mathematics and Computer Science, 2011)

[EN] Each Dirichlet series D=∑∞n=1an1nsD=∑n=1∞an1ns, with variable s∈Cs∈C and coefficients an∈Can∈C, has a so called Bohr strip, the largest strip in CC on which DD converges absolutely but not uniformly. The classical ...

[EN] Recent results on Dirichlet series Sigma(n) a(n) 1/n(s), s is an element of C, with coefficients a(n) in an infinite dimensional Banach space X show that the maximal width of uniform but not absolute convergence ...

[EN] 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) f complex null sequences. ...

Conejero, J. Alberto; Seoane-Sepulveda, Juan B.; Sevilla Peris, Pablo(John Wiley & Sons, 2017)

[EN] We employ a classical result by Toeplitz (1913) and the seminal work by Bohnenblust and Hille on Dirichlet series (1931) to show that the set of continuous m-homogeneous non-analytic polynomials on c(o) contains an ...

Defant, Andreas; Sevilla Peris, Pablo(Adam Mickiewicz University The Faculty of Mathematics and Computer Science, 2014)

[EN] In 1931 H.F.Bohnenblust and E.Hille published a very important paper in which
not only did they solve a long standing problem on convergence of Dirichlet series, but also
gave a general version of a celebrated ...

Carando, Daniel; Defant, Andreas; García, Domingo; Maestre, Manuel; Sevilla Peris, Pablo(Polskiej Akademii Nauk, Instytut Matematyczny (Polish Academy of Sciences, Institute of Mathematics), 2015)

[EN] Denote by Ω(n) the number of prime divisors of n ∈ N
(counted with multiplicities). For x ∈ N define the Dirichlet-Bohr radius
P
L(x) to be the best r > 0 such that for every finite Dirichlet polynomial
n≤x
...

Bonet Solves, José Antonio(Cambridge University Press, 2018)

[EN] 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 ...