EUDML

Estudiamos algunas situaciones donde encontramos un problema que, a primera vista, parece no tener solución. Pero, de hecho, existe un subespacio vectorial grande de soluciones del mismo.

Products of holomorphically relevant spaces

Maestre, Manuel — 1987

Portugaliae mathematica

Extension of multilinear mappings on Banach spaces

Pablo Galindo; Domingo Garciá; Manuel Maestre; Jorge Mujica — 1994

Studia Mathematica

Integral holomorphic functions

Verónica Dimant; Pablo Galindo; Manuel Maestre; Ignacio Zalduendo — 2004

Studia Mathematica

We define the class of integral holomorphic functions over Banach spaces; these are functions admitting an integral representation akin to the Cauchy integral formula, and are related to integral polynomials. After studying various properties of these functions, Banach and Fréchet spaces of integral holomorphic functions are defined, and several aspects investigated: duality, Taylor series approximation, biduality and reflexivity.

The Daugavet equation for polynomials

Yun Sung Choi; Domingo García; Manuel Maestre; Miguel Martín — 2007

Studia Mathematica

We study when the Daugavet equation is satisfied for weakly compact polynomials on a Banach space X, i.e. when the equality ||Id + P|| = 1 + ||P|| is satisfied for all weakly compact polynomials P: X → X. We show that this is the case when X = C(K), the real or complex space of continuous functions on a compact space K without isolated points. We also study the alternative Daugavet equation $m a x_{| ω | = 1} | | I d + ω P | | = 1 + | | P | |$ for polynomials P: X → X. We show that this equation holds for every polynomial on the complex space X =...

The Dirichlet-Bohr radius

Daniel Carando; Andreas Defant; Domingo A. Garcí; Manuel Maestre; Pablo Sevilla-Peris — 2015

Acta Arithmetica

Denote by Ω(n) the number of prime divisors of n ∈ ℕ (counted with multiplicities). For x∈ ℕ define the Dirichlet-Bohr radius L(x) to be the best r > 0 such that for every finite Dirichlet polynomial $\sum_{n \leq x} a_{n} n^{- s}$ we have $\sum_{n \leq x} | a_{n} | r^{Ω (n)} \leq s u p_{t \in ℝ} | \sum_{n \leq x} a_{n} n^{- i t} |$ . We prove that the asymptotically correct order of L(x) is ${(l o g x)}^{1 / 4} x^{- 1 / 8}$ . Following Bohr’s vision our proof links the estimation of L(x) with classical Bohr radii for holomorphic functions in several variables. Moreover, we suggest a general setting which allows translating various results on Bohr...