Mirta Castro - Academia.edu (original) (raw)

Papers by Mirta Castro

Orthogonal matrix polynomials satisfying first order differential equations: a collection of inst... more Orthogonal matrix polynomials satisfying first order differential equations: a collection of instructive examples

Recently, some sufficient and necessary conditions have been given on the convergence of the so-c... more Recently, some sufficient and necessary conditions have been given on the convergence of the so-called vector Stieltjes continued fraction of dimension p in terms of the coefficients. In the present paper we aim to continue this study for the case of dimension 2. In particular, we show that here the convergence is determined by the asymptotics of solutions of a particular three-term recurrence relation, which is closely analyzed. As a consequence, several new results on the convergence problem for two-dimensional Stieltjes continued fractions are obtained. We finally describe the link to a vector moment problem.

Le Journal de Physique Colloques, 1988

Symmetry, Integrability and Geometry: Methods and Applications, 2013

ABSTRACT The use of spectral methods to study birth-and-death processes was pioneered by S. Karli... more ABSTRACT The use of spectral methods to study birth-and-death processes was pioneered by S. Karlin and J. McGregor. Their expression for the transition probabilities was made explicit by them in a few cases. Here we complete their analysis and indicate a few applications of their very powerful method.

Journal of Nonlinear Mathematical Physics, 2005

ABSTRACT We describe a few families of orthogonal matrix polynomials of size N × N satisfying fir... more ABSTRACT We describe a few families of orthogonal matrix polynomials of size N × N satisfying first order differential equations. This problem differs from the recent efforts reported for instance in [7] (Orthogonal matrix polynomials satisfying second order differential equations, Internat. Math. Research Notices, 2004 : 10 (2004), 461-484) and [15] (Matrix valued orthogonal polynomials of the Jacobi type, Indag. Math. 14 nrs. 3, 4 (2003), 353-366). While we restrict ourselves to considering only first order operators, we do not make any assumption as to their symmetry. For simplicity we restrict to the case N = 2. We draw a few lessons from these examples; many of them serve to illustrate the fundamental difference between the scalar and the matrix valued case.

Journal of Approximation Theory, 2000

We consider complex Jacobi matrices G which can be decomposed in the form G=J+C, where J is a rea... more We consider complex Jacobi matrices G which can be decomposed in the form G=J+C, where J is a real Jacobi matrix and C is a complex Jacobi matrix whose entries are uniformly bounded. We prove that the determinacy of the operator defined by G is equivalent to that of J. From this we deduce that the determinacy of G is

Integral Transforms and Special Functions, 2012

We introduce a family of weight matrices W of the form T (t)T * (t), T (t) = e A t e Dt 2 , where... more We introduce a family of weight matrices W of the form T (t)T * (t), T (t) = e A t e Dt 2 , where A is certain nilpotent matrix and D is a diagonal matrix with negative real entries. The weight matrices W have arbitrary size N × N and depend on N parameters.

Integral Equations and Operator Theory, 2007

ABSTRACT Given a weight matrix W(x) of size N on the real line one constructs a sequence of matri... more ABSTRACT Given a weight matrix W(x) of size N on the real line one constructs a sequence of matrix valued orthogonal polynomials, {P n } n≥0. We study the algebra D(W){\mathcal{D}}(W) of differential operators D with matrix coefficients such that P n D = Λ n P n , with Λ n in the algebra A of N × N complex matrices. We study certain representations of this algebra, prove that it is a *-algebra and give a precise description of its isomorphic image inside the algebra AN0{A^{{N}_0}} .

Constructive Approximation, 2008