García, Domingo; Jorda Mora, Enrique; Maestre, Manuel(Elsevier, 2017-01-15)
[EN] In this paper we give a new characterization of when a Banach space E has the Schur property in terms of the disk algebra. We prove that E has the Schur property if and only if A(D, E) = A(D,E-w). (C) 2016 Elsevier ...
[EN] In this paper we give general conditions on a countable family V of weights on an unbounded open set U in a complex Banach space X such that the weighted space HV (U) of holomorphic functions on U has a Frechet algebra ...
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] We study composition operators on spaces of double Dirichlet series, focusing our interest on the characterization of the composition operators of the space of bounded double Dirichlet series H infinity(C+2) We also ...
[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. ...
For two complex Banach spaces X and Y, in this paper, we study the generalized spectrum M-b(X,Y) of all nonzero algebra homomorphisms from H-b(X), the algebra of all bounded type entire functions on X into H-b(Y). We endow ...
[EN] Let H-infinity be the set of all ordinary Dirichlet series D = Sigma(n) a(n)(n-1) ann-s representing bounded holomorphic functions on the right half plane. A completely multiplicative sequence (b(n)) of complex numbers ...
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
...