Author profile: Álvarez Nodarse, Renato
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Name  Álvarez Nodarse, Renato 
Department  Análisis Matemático 
Knowledge area  Análisis Matemático 
Professional category  Catedrático de Universidad 
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Publications 

Final Degree Project
El teorema de muestreo y sus aplicaciones
(20180901)
En este trabajo nuestro objeto de estudio será la teoría de señales, el objetivo es llegar al teorema de muestreo de ... 
Article
Uniform convergence of basic FourierBessel series on a qlinear grid
(Springer, 20180901)
We study FourierBessel series on a qlinear grid, defined as expansions in complete qorthogonal systems constructed with ... 
Presentation
Functionals of harmonics functions
(Multidisciplinary Digital Publishing Institute, 20180101)
Let CsT, with T > 0, be the set of continuous, Tperiodic functions f : R → Rs, and let Γ : CsT → R be a real functional on CsT. 
Presentation
On qpolynomials and some of their applications
(20160101)

Article
On linearly related sequences of difference derivatives of discrete orthogonal polynomials
(Elsevier, 20150815)
Let ν be either ω ∈ C \ {0} or q ∈ C \ {0, 1}, and let Dν be the corresponding difference operator defined in the usual ... 
Article
General approach for dealing with dynamical systems with spatiotemporal periodicities
(American Physical Society, 20150101)
Dynamical systems often contain oscillatory forces or depend on periodic potentials. Time or space periodicity is reflected ... 
Article
Paramagnetic colloidal ribbons in a precessing magnetic field
(American Physical Society, 20150101)
We investigate the dynamics of a kink in a damped parametrically driven nonlinear KleinGordon equation.We show by using ... 
PhD Thesis
Orthogonal matrix polynomials and differential, difference and qdifference matrix operators
(20140905)
In this thesis we present a series of result that are framed in the theory of Matrix Orthogonal Polynomials, a branch of ... 
Article
On the limit of nonstandard qRacah polynomials
(20140315)
The aim of this article is to study the limit transitions from nonstandard qRacah polynomials to big qJacobi, dual ... 
Article
Kink topology control by highfrequency external forces in nonlinear KleinGordon models
(American Physical Society, 20140101)
A method of averaging is applied to study the dynamics of a kink in the damped double sineGordon equation driven by both ... 
Article
On the properties of special functions on the lineartype lattices
(Elsevier, 20130901)
We present a general theory for studying the difference analogues of special functions of hypergeometric type on the ... 
Article
On the generalized AskeyWilson polynomials
(Elsevier, 20130601)
In this paper a generalization of AskeyWilson polynomials is introduced. These polynomials are obtained from the AskeyWilson ... 
Article
Timeshift invariance determines the functional shape of the current in dissipative rocking ratchets
(20130101)
Ratchets are devices that are able to rectify an otherwise oscillatory behavior by exploiting an asymmetry of the system. ... 
Article
Comment on “Ratchet universality in the presence of thermal noise”
(20130101)
A recent paper [P. J. Martínez and R. Chacón, Phys. Rev. E 87, 062114 (2013)] presents numerical simulations on a system ... 
Article
Propulsion efficiency of a dynamic selfassembled helical ribbon
(20130101)
We study the dynamic selfassembly and propulsion of a ribbon formed from paramagnetic colloids in a dynamic magnetic ... 
Article
The qRacahKralltype polynomials
(Elsevier, 20120801)
In this paper the Kralltype polynomials obtained via the addition of two mass points to the weight function of the standard ... 
Article
Spectral properties of certain tridiagonal matrices
(Elsevier, 20120201)
We study spectral properties of irreducible tridiagonal k−Toeplitz matrices and certain matrices which arise as perturbations of them. 
Presentation
El efecto ratchet en la partícula relativista
(20120101)

Presentation
La corriente promedio en los ”rocking ratchets”
(20120101)

Article
On the orthogonality of qclassical polynomials of the Hahn class
(20120101)
The central idea behind this review article is to discuss in a unified sense the orthogonality of all possible polynomial ... 
Article
À la carte recurrence relations for continuous and discrete hypergeometric functions
(Sociedad Española de Matemática Aplicada, 20110901)
We show how, using the constructive approach for special functions introduced by Nikiforov and Uvarov, one can obtain ... 
Article
On the Kralltype polynomials on qquadratic lattices
(Elsevier, 20110801)
In this paper, we study the Kralltype polynomials on nonuniform lattices. For these polynomials the second order linear ... 
Article
Ratchet effect on a relativistic particle driven by external forces
(Institute of Physics, 20110101)
We study the ratchet effect of a damped relativistic particle driven by both asymmetric temporal biharmonic and timeperiodic ... 
Article
Symmetries shape the current in ratchets induced by a biharmonic driving force
(20100323)
Equations describing the evolution of particles, solitons, or localized structures, driven by a zeroaverage, periodic, ... 
Article
Symmetries shape the current in ratchets induced by a biharmonic driving force [Rapid Comunication]
(American Physical Society, 20100101)
Equations describing the evolution of particles, solitons, or localized structures, driven by a zeroaverage, periodic, ... 
Article
Driven and damped double sineGordon equation: The influence of internal modes on the soliton ratchet mobility
(20090101)
This work studies the damped double sineGordon equation driven by a biharmonic force, where a parameter λ controls the ... 
Article
Structural and recurrence relations for hypergeometrictype functions by NikiforovUvarov method
(Kent State University, 20090101)
The functions of hypergeometrictype are the solutions y = yν(z) of the differential equation σ(z)y ′′ + τ(z)y ′ + λy = ... 
Article
A characterization of the classical orthogonal discrete and qpolynomials
(Elsevier, 20070401)
In this paper we present a new characterization for the classical discrete and qclassical (discrete) polynomials (in the Hahn's sense). 
Article 
Article
On characterizations of classical polynomials
(Elsevier, 20061101)
It is well known that the classical families of Jacobi, Laguerre, Hermite, and Bessel polynomials are characterized as ... 
Article
Special volume on orthogonal polynomials and mathematical physics
(Kent State University, 20060101)

Article
A qanalog of the Racah polynomials and the qalgebra SUq(2)
(Springer, 20060101)
We study some qanalogues of the Racah polynomials and some of their applications in the theory of representation of quantum algebras. 
Article
Modelos matemáticos en biología: un viaje de ida y vuelta
(Sociedad Española de Matemática Aplicada, 20060101)
El objetivo de este trabajo es mostrar la provechosa interacción entre la Biología y la Matemática. Para ello veremos cómo, ... 
Article
Limit relations between qKrall type orthogonal polynomials
(Elsevier, 20060101)
In this paper, we consider a natural extension of several results related to Kralltype polynomials introducing a modification ... 
Article
On recurrence relations for radial wave functions for the Nth dimensional oscillators and hydrogenlike atoms: analytical and numerical study
(20060101)
Using a general procedure for finding recurrence relations for hypergeometric functions and polynomials introduced by ... 
Article
On some tridiagonal kToeplitz matrices: algebraic and analytical aspects. Applications
(Elsevier, 20051215)
In this paper we use the analytic theory for 2 and 3Toeplitz matrices to obtain the explicit expressions for the eigenvalues, ... 
Article
On a qextension of the linear harmonic oscillator with the continuous orthogonality property on R
(Springer, 20051101)
We discuss a qanalogue of the linear harmonic oscillator in quantum mechanics, based on a qextension of the classical ... 
Article
Factorization of the hypergeometrictype difference equation on the nonuniform lattices: dynamical algebra
(Institute of Physics, 20050107)
We argue that one can factorize the difference equation of hypergeometric type on the nonuniform lattices in general case. ... 
Article
Recurrence relations for discrete hypergeometric functions
(Taylor & Francis, 20050101)
We present a general procedure for finding linear recurrence relations for the solutions of the second order difference equation of hypergeometric type. Applications to wave functions of certain discrete system are also given. 
Article
On the Kralltype discrete polynomials
(Elsevier, 20040701)
In this paper we present a unified theory for studying the so called Kralltype discrete orthogonal polynomials. In particular, ... 
Article
Asymptotic properties of generalized Laguerre orthogonal polynomials
(Elsevier, 20040601)
In the present paper we deal with the polynomials L(α,M,N) n (x) orthogonal with respect to the Sobolev inner product (p, ... 
Article
Modifications of quasidefinite linear functionals via addition of delta and derivatives of delta Dirac functions
(Elsevier, 20040101)
We consider the general theory of the modifications of quasidefinite linear functionals by adding discrete measures. We ... 
Article
On the Kralltype polynomials
(20040101)
Using a general and simple algebraic approach, some results on Kralltype orthogonal polynomials and some of their extensions are obtained. 
Article
A qextension of the generalized Hermite polynomials with the continuous orthogonality property on R
(Academic Publications, 20040101)
In this paper we study in detail a qextension of the generalized Hermite polynomials of Szeg˝o. A continuous orthogonality ... 
Article
Some limit relations in the A1 tableau of DunklCherednik operators
(Elsevier, 20031215)
In this paper we study some limit relations involving some qspecial functions related with the A1 (root system) tableau ... 
Article
Mellin transforms for some families of qpolynomials
(Elsevier, 20030401)
By using Ramanujan's qextension of the Euler integral representation for the gamma function, we derive the Mellin integral ... 
Article
On a qextension of the Hermite polynomials Hn(x) with the continuous orthogonality property on R1
(Sociedad Matemática Mexicana / Springer, 20021001)
We study a polynomial sequence of qextensions of the classical Hermite polynomials Hn(x), which satisfi es continuous ... 
Article
Distribution of zeros of discrete and continuous polynomials from their recurrence relation
(Elsevier, 20020525)
The hypergeometric polynomials in a continous or a discrete variable, whose canonical forms are the socalled classical ... 
Article
On a modification of the Jacobi linear functional asymptotic properties and zeros of the corresponding orthogonal polynomials
(Springer, 20020401)
The paper deals with orthogonal polynomials in the case where the orthogonality condition is related to semiclassical ... 
Article
qClassical polynomials and the qAskey and NikiforovUvarov tableaus
(Elsevier, 20011015)
In this paper we continue the study of the qclassical (discrete) polynomials (in the Hahn's sense) started in Medem et ... 
Article
On the qpolynomials: a distributional study
(Elsevier, 20011015)
In this paper we present a uni1ed distributional study of the classical discrete qpolynomials (in the Hahn’s sense). From ... 
Article
Factorization method for difference equations of hypergeometric type on nonuniform lattices
(IOP Publishing, 20010629)
We study the factorization of the hypergeometrictype difference equation of Nikiforov and Uvarov on nonuniform lattices. An explicit form of the raising and lowering operators is derived and some relevant examples are given. 
Article
On the connection and linearization problem for discrete hypergeometric qpolynomials
(Elsevier, 20010501)
In the present paper, starting from the secondorder difference hypergeometric equation on the nonuniform lattice x(s) ... 
Article
On the "Favard theorem" and its extensions
(Elsevier, 20010115)
In this paper we present a survey on the "Favard theorem" and its extensions. 
Article
Polinomios ortogonales: historia y aplicaciones
(Sociedad Española de Matemática Aplicada, 20010101)

Chapter of Book
Los qpolinomios hipergeométricos
(Universidad de La Rioja, 20010101)
It is well known that the qpolynomials of hypergeometric type are the polynomial solutions of a certain second order ... 
Article
On the linearization problem involving Pochhammer symbols and their qanalogues
(Elsevier, 19990715)
In this paper we present a simple recurrent algorithm for solving the linearization problem involving some families of qpolynomials in the exponential lattice x(s)=c1qs+c3. Some simple examples are worked out in detail. 
Article
On the qpolynomials on the exponential lattice x(s)= c 1 qs + c 3
(Taylor & Francis, 19990101)
The main goal of this paper is to continue the study of the qpolynomials on nonuniform lattices by using the approach ... 
Article
Second order difference equations for certain families of discrete polynomials
(Elsevier, 19981116)
In this paper we will consider two algorithms which allow us to obtain second order linear di erence equations for certain ... 
Article
WKB approximation and KrallType orthogonal polynomials
(Springer, 19981001)
We give an uni ed approach to the Kralltype polynomials orthogonal with respect to a positive measure consisting of an ... 
Article
JacobiSobolevtype orthogonal polynomials: secondorder differential equation and zeros
(Elsevier, 19980417)
We obtain an explicit expression for the Sobolevtype orthogonal polynomials {Qn} associated with the inner product ... 
Article
Modified ClebschGordantype expansions for products of discrete hypergeometric polynomials
(Elsevier, 19980309)
Starting from the secondorder difference hypergeometric equation satisfied by the set of discrete orthogonal polynomials ... 
Article
On the modification of classical orthogonal polynomials: the symmetric case
(Springer, 19980301)
We consider the modifcations of the monic Hermite and Gegenbauer polynomials via the addition of one point mass at the ... 
Article
Some extension of the Besseltype orthogonal polynomials
(Taylor & Francis, 19980101)
We consider the perturbation of the classical Bessel moment functional by the addition of the linear functional M0 (x) + ... 
Article
The distribution of zeros of general qpolynomials
(Institute of Physics, 19971007)
A general system of qorthogonal polynomials is de ned by means of its threeterm recurrence relation. This system encompasses ... 
Article
The limit relations between generalized orthogonal polynomials
(Elsevier, 19970901)
We consider the different limit transitions for modifications of the classical polynomials obtained by the addition of one ... 
Article
Recurrence relations for connection coefficients between qorthogonal polynomials of discrete variables in the nonuniform lattice X(s) = q2s
(Institute of Physics, 19961121)
We obtain the structure relations for qorthogonal polynomials in the exponential lattice q 2s and from that we construct ... 
Article
The dual Hahn qpolynomials in the lattice x(s) = [s]q[s + 1] q and the qAlgebras SUq(2) and SUq(1; 1)
(Institute of Physics, 19960407)
The dual qHahn polynomials in the non uniform lattice x(s) = [s]q[s + 1]q are obtained. The main data for these polynomials ... 
Article
On the properties for modifications of classical orthogonal polynomials of discrete variables
(Elsevier, 19951229)
We consider a modi cation of moment functionals for some classical polynomials of a discrete variable by adding a mass ... 
Article
A generalization of the classical Laguerre polynomials
(Springer, 19950101)
We consider a modi cation of the gamma distribution by adding a discrete measure supported in the point x = 0. For large ... 
Article
The modification of classical Hahn polynomials of a discrete variable
(Taylor & Francis, 19950101)
We consider a modi cation of moment functionals for the Hahn classical polynomials of a discrete variable by adding two ... 
Article
qDeformed Vibron model for diatomic molecules
(American Physical Society, 19940801)
A deformed version of the vibron model for diatomic molecules is constructed. Both the O(4) and U(3) dynamical symmetries ... 