Matrix Sylvester equations in the theory of orthogonal polynomials on the unit circle

Branquinho, A.; Rebocho, M. N.

http://hdl.handle.net/10400.6/9055

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Authors

Branquinho, A.

Rebocho, M. N.

Abstract(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.

Keywords

Orthogonal polynomials on the unit circle Matrix Sylvester differential equations Matrix Riccati differential equations Measures on the unit circle Semi-classical class

URI

http://hdl.handle.net/10400.6/9055

Citation

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.