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

DOI

10.2991/jnmp.2005.12.s2.6How to use a DOI?

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

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Mirta M. Castro
AU  - F. Alberto GRUNBAUM
PY  - 2005
DA  - 2005/12/01
TI  - Orthogonal matrix polynomials satisfying first order differential equations: a collection of instructive examples
JO  - Journal of Nonlinear Mathematical Physics
SP  - 63
EP  - 76
VL  - 12
IS  - Supplement 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.s2.6
DO  - 10.2991/jnmp.2005.12.s2.6
ID  - Castro2005
ER  -