17 citations · 29 across the 15 of their papers we have counts for
19 papers
Universality arising from invertible weighted composition operators
Luciano Abadías, F. Javier González-Doña, Jesús Oliva-Maza
A linear operator acting boundedly on an infinite-dimensional separable complex Hilbert space is universal if every linear bounded operator acting on is similar to a sc…
Discrete Besov spaces via semigroups associated to the discrete Laplacian and regularity of non-local operators
Luciano Abadias, Marta De León-Contreras, Alejandro Mahillo
In this paper we prove characterizations of the discrete Besov spaces in terms of the heat and Poisson semigroups associated with the discrete Laplacian that will allow us to prove…
Large time behaviour for the heat equation on moments and decay rates
Luciano Abadias, Jorge González-Camus, Pedro J. Miana +1
The paper is devoted to understand the large time behaviour and decay of the solution of the discrete heat equation in the one dimensional mesh on spaces, and its ana…
Discrete Hölder spaces, their characterization via semigroups associated to the discrete Laplacian and kernels estimates
Luciano Abadias, Marta De León-Contreras
In this paper we characterize the discrete Hölder spaces by means of the heat and Poisson semigroups associated to the discrete Laplacian. These characterizations allow us to get r…
Subordination principle, Wright functions and large-time behaviour for the discrete in time fractional diffusion equation
Luciano Abadias, Edgardo Alvarez, Stiven Diaz
The main goal in this paper is to study asymptotic behaviour in for the solutions of the fractional version of the discrete in time -dimensional diffusion eq…
Asymptotic behavior for the discrete in time heat equation
Edgardo Alvarez, Luciano Abadias
In this paper we investigate the asymptotic behavior and decay of the solution of the discrete in time -dimensional heat equation. We give a convergence rate with which the solu…
Fractional-order susceptible-infected model: definition and applications to the study of COVID-19 main protease
Luciano Abadias, Gissell Estrada-Rodriguez, Ernesto Estrada
We propose a model for the transmission of perturbations across the amino acids of a protein represented as an interaction network. The dynamics consists of a Susceptible-Infected…
Functional models up to similarity and -contractions
Luciano Abadias, Glenier Bello, Dmitry Yakubovich
We study the generalization of -isometries and -contractions (for positive integers ) to what we call -isometries and -contractions for positive real numbers . We…
Poisson equation and discrete one-sided Hilbert transform for -bounded operators
Luciano Abadias, José E. Galé, Carlos Lizama
We characterize the solutions of the Poisson equation and the domain of its associated one-sided Hilbert transform for Cesàro bounded operators of fractional order. The results obt…
Operator inequalities I. Models and ergodicity
Luciano Abadias, Glenier Bello-Burguet, Dmitry Yakubovich
We discuss when an operator, subject to a rather general inequality in hereditary form, admits a unitarily equivalent functional model of Agler type in the reproducing kernel Hilbe…
Growth orders and ergodicity for absolutely Cesàro bounded operators
Luciano Abadias, Antonio Bonilla
In this paper, we extend the concept of absolutely Cesàro boundedness to the fractional case. We construct a weighted shift operator belonging to this class of operators, and we pr…
Schauder estimates for discrete fractional integrals
Luciano Abadias, Marta De León-Contreras, José L. Torrea
In this note we focus on the discrete fractional integrals as a natural continuation of our previous work about nonlocal fractional derivatives, discrete and continuous. We define…
On well-posedness of vector-valued fractional differential-difference equations
Luciano Abadias, Carlos Lizama, Pedro J. Miana +1
We develop an operator-theoretical method for the analysis on well posedness of partial differential equations that can be modeled in the form \begin{equation*} \left\{ \begin{arra…
A Katznelson-Tzafriri type theorem for Cesàro bounded operators
Luciano Abadias
We extend the well-known Katznelson-Tzafriri theorem, originally posed for power-bounded operators, to the case of Cesàro bounded operators of any order For this purpose, we…
Sharp extensions and algebraic properties for solution families of vector-valued differential equations
Luciano Abadias, Carlos Lizama, Pedro J. Miana
In this paper we show the unexpected property that extension from local to global without loss of regularity holds for the solutions of a wide class of vector-valued differential e…
Cesáro sums and algebra homomorphisms of bounded operators
Luciano Abadias, Carlos Lizama, Pedro J. Miana +1
Let be a complex Banach space. The connection between algebra homomorphisms defined on subalgebras of the Banach algebra and the algebraic structure of…
A subordination principle on Wright functions and regularized resolvent families
Luciano Abadias, Pedro J. Miana
We obtain a vector-valued subordination principle for -regularized resolvent families which unified and improves various previous results in the literature. As a conseq…
Quadrature rules for -weighted norms of orthogonal polynomials
Luciano Abadias, Pedro J. Miana, Natalia Romero
In this paper we obtain -weighted norms of classical orthogonal polynomials (Hermite, Laguerre and Jacobi polynomials) in terms of the zeros of these orthogonal polynomials; t…
Hermite expansions of -groups and cosine functions
Luciano Abadias, Pedro J. Miana
In this paper we introduce vector-valued Hermite expansions to approximate one-parameter operator families such as -groups and cosine functions. In both cases we estimate the…