CIEM 05476
CENTRO DE INVESTIGACION Y ESTUDIOS DE MATEMATICA
Unidad Ejecutora - UE
artículos
Título:
The algebra of differential operators associated to a weight matrix: a first example
Autor/es:
JUAN TIRAO
Revista:
CONTEMPORARY MATHEMATICS
Editorial:
American Mathematical Society
Referencias:
Año: 2011 vol. 537 p. 291 - 324
ISSN:
0271-4132
Resumen:
Given a weight matrix W(t) of size N on the real line one constructs a sequence of matrix valued orthogonal polynomials (Pn). Then one may be interested in studying the algebra D(W) of all differential operators with matrix coefficients such that PnD=Ln(D)Pn with Ln(D) a constant matrix. In this paper we consider matrix valued orthogonal polynomials going along with a weight matrix of size 2 of the Hermite type. The purpose of this paper is to compute in this case the algebra D(W) and to study its structure. In particular we give an algebraic proof of some results conjectured by M. Castro and F.A. Grunbaum.
