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Autores
Orientador(es)
Resumo(s)
In this paperwe 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.
Descrição
Palavras-chave
Orthogonal polynomials on the unit circle Matrix Sylvester differential equations Matrix Riccati differential equations Measures on the unit circle Semi-classical class
Contexto Educativo
Citação
A. Branquinho and M.N. Rebocho, Matrix Sylvester equations in the theory of orthogonal polynomials on the unit circle, Bulletin of the Belgian Mathematical Society - Simon Stevin 17 (2010), 355-376.