Volume 12, Issue Supplement 2, December 2005, Pages 63 - 76
Orthogonal matrix polynomials satisfying first order differential equations: a collection of instructive examples
Mirta M CASTRO, F Alberto GRUNBAUM
Mirta M CASTRO
Available Online 1 December 2005.
- https://doi.org/10.2991/jnmp.2005.12.s2.6How to use a DOI?
- 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  (Orthogonal matrix polynomials satisfying second order differential equations, Internat. Math. Research Notices, 2004 : 10 (2004), 461484) and  (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.
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Cite this article
TY - JOUR AU - Mirta M CASTRO AU - F Alberto GRUNBAUM PY - 2005 DA - 2005/12 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 - https://doi.org/10.2991/jnmp.2005.12.s2.6 ID - CASTRO2005 ER -