[EN] The Bohr–Bohnenblust–Hille theorem states that the width of the strip in the complex plane on which an
ordinary Dirichlet series P
n
ann
−s
converges uniformly but not absolutely is less than or equal to 1
2
, ...
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 ...
Defant, Andreas; Sevilla Peris, Pablo(Oxford University Press (OUP), 2012-09)
[EN] If E is a Banach sequence space, then each holomorphic function defines a formal power series ¿ ¿ c ¿(f) z ¿. The problem of when such an expansion converges absolutely and actually represents the function goes back ...
[EN] We study extendibility of diagonal multilinear operators from l(p) to l(p) spaces. We determine the values of and for which every diagonal -linear operator is extendible, and those for which the only extendible ones ...
[EN] We estimate the -norm of finite Dirichlet polynomials with coefficients in a Banach space. Our estimates quantify several recent results on Bohr's strips of uniform but non absolute convergence of Dirichlet series in ...
DANIEL CARANDO; Sevilla Peris, Pablo(Springer Verlag (Germany), 2014-03)
[EN] We study Hahn-Banach extensions of multilinear forms defined on Banach sequence spaces. We characterize c(0) in terms of extension of bilinear forms, and describe the Banach sequence spaces in which every bilinear ...
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 G.; García Rodríguez, Domingo; Maestre Vera, Manuel; Sevilla Peris, Pablo(American Mathematical Society, 2012)
In this paper we survey the most relevant recent developments
on the research of the spectra of algebras of analytic functions. We concentrate
mainly in three algebras, the Banach algebra H∞(B) of all bounded
holomorphic ...
[EN] We introduce non-linear versions of the classical cotype of Banach spaces. We show that spaces with l.u.st. and cotype, and spaces having Fourier cotype enjoy our non-linear cotype. We apply these concepts to get ...
Dimant, Verónica; Sevilla Peris, Pablo(Universitat Autonoma de Barcelona, 2016)
[EN] We investigate the summability of the coefficients of m-homogeneous polynomials and m-linear mappings defined on l(p) spaces. In our research we obtain results on the summability of the coefficients of m-linear mappings ...
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 ...
We give a variant of the Bohenblust-Hille inequality which, for certain families of polynomials, leads to constants with polynomial growth in the degree.
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
...
Defant, Andreas; Sevilla Peris, Pablo(Institute of Mathematics, Polish Academy of Sciences, 2016)
[EN] Let x(m, n) be the unconditional basis constant of the monomial basis Z alpha, alpha is an element of N(0)n with vertical bar alpha vertical bar = m, of the Banach space of all m-homogeneous polynomials inn complex ...