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Listar por palabra clave "Dirichlet series"

Mostrando ítems 1-10 de 10

A note on abscissas of Dirichlet series

Defant, Andreas; Pérez, Antonio; Sevilla Peris, Pablo (Springer-Verlag, 2019-07)

[EN] We present an abstract approach to the abscissas of convergence of vector-valued Dirichlet series. As a consequence we deduce that the abscissas for Hardy spaces of Dirichlet series are all equal. We also introduce ...
Bohr's strips for Dirichlet series in Banach spaces

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 ...
Convergence of Dirichlet polynomials in Banach spaces

Defant, Andreas; Sevilla Peris, Pablo (American Mathematical Society, 2011-02)

[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 ...
Dirichlet series from the infinite dimensional point of view

Defant, A.; García, Domingo; Maestre, Manuel; Sevilla Peris, Pablo (Adam Mickiewicz University, 2018-12)

[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. ...
Hardy space of translated Dirichlet series

Fernández Vidal, Tomás; Galicer, Daniel; Mereb, Martín; Sevilla Peris, Pablo (Springer-Verlag, 2021-10)

[EN] We study the Hardy space of translated Dirichlet series H+. It consists on those Dirichlet series Sigma a(n)n(-s) such that for some (equivalently, every) 1 <= p < infinity, the translation Sigma a(n)n(-(s+ 1/sigma)) ...
Isomorphic copies of l(1) for m-homogeneous non-analytic Bohnenblust-Hille polynomials

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 ...
Norm Attaining Elements of the Ball Algebra H-infinity(B-N)

Aron, Richard M.; Bonet Solves, José Antonio; Maestre, Manuel (Springer-Verlag, 2024-03)

[EN] Let B(N )be the Euclidean ball of C-N. The space H-infinity(B-N) of bounded holomorphic functions on B-N is known to have a predual, denoted by G(infinity)(B-N). We study the functions in H-infinity(B-N) that attain ...
The Bohnenblust Hille cycle of ideas from a modern point of view

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 ...
The Dirichlet-Bohr radius

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 ...
THE FRECHET SCHWARTZ ALGEBRA OF UNIFORMLY CONVERGENT DIRICHLET SERIES

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 ...