Atlantis Press Paper Details: Orthogonal matrix polynomials satisfying first order differential equations: a collection of instructive examples

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), 461484) and [15] (Matrix valued orthogonal polynomials of the Jacobi type, Indag. Math. 14 nrs. 3, 4 (2003), 353366). 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.


title:		Orthogonal matrix polynomials satisfying first order differential equations: a collection of instructive examples
publication:		JNMP
volume-issue:		12 - Supplement 2
pages:		63 - 76
ISSN:		1402-9251
DOI:		doi:10.2991/jnmp.2005.12.s2.6 (how to use a DOI)
author(s):		Mirta M CASTRO, F Alberto GRUNBAUM
publication date:		December 2005
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), 461484) and [15] (Matrix valued orthogonal polynomials of the Jacobi type, Indag. Math. 14 nrs. 3, 4 (2003), 353366). 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.
copyright:		© Atlantis Press. This article is distributed under the terms of the Creative Commons Attribution License, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited.
full text:		12s2_06n.pdf (145 K)