In this paper we characterize sequences of orthogonal polynomials
on the unit circle whose Carathéodory function
satisfies a Riccati differential equation with polynomial
coefficients, in terms of matrix Sylvester differential
equations.
For the particular case of semi-classical orthogonal polynomials on
the unit circle, it is derived a characterization
in terms of first order linear differential systems.
Publié le : 2010-04-15
Classification:
Carathéodory function,
matrix Riccati differential equations,
matrix Sylvester differential equations,
measures on the unit circle,
semi-classical class,
33C45,
39B42
@article{1274896211,
author = {Branquinho, A. and Rebocho, M.N.},
title = {Matrix Sylvester equations in the theory of orthogonal polynomials on the unit circle},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {17},
number = {1},
year = {2010},
pages = { 355-376},
language = {en},
url = {http://dml.mathdoc.fr/item/1274896211}
}
Branquinho, A.; Rebocho, M.N. Matrix Sylvester equations in the theory of orthogonal polynomials on the unit circle. Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, pp. 355-376. http://gdmltest.u-ga.fr/item/1274896211/