The algebra of differential operators associated to a wieght matrix

F.A.GRUNBAUM AND J. TIRAO

INTEGRAL EQUATIONS AND OPERATOR THEORY

Birkhäuser Verlag

Lugar: Basel, Switzerland; Año: 2007 vol. 58 p. 449 - 475

0378-620X

Given a weight matrix W(x) of size N on the real line one constructs a sequence of matrix valued orthogonal polynomials P_n . We study the algebra D(W) of differential operators D with matrix coefficients such that P_n D=Lambda_n P_n, with Lambda_n in the algebra A of N x 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 A^{N_0} a countable direct product of copies of the algebra A.