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- Characterizations of Laguerre-Hahn affne orthogonal polynomials on the unit circlePublication . Branquinho, A.; Rebocho, M. N.In this work we characterize a monic polynomial sequence, orthogonal with respect to a hermitian linear functional [...]
- Structure relations for orthogonal polynomials on the unit circlePublication . Branquinho, A.; Rebocho, M. N.Structure relations for orthogonal polynomials on the unit circle are studied. We begin by proving that semi-classical orthogonal polynomials on the unit circle satisfy structure relations of the following type: [...]
- On differential equations for orthogonal polynomials on the unit circlePublication . Branquinho, A.; Rebocho, M. N.In this paper we characterize sequences of orthogonal polynomials on the unit circle whose corresponding Carathéodory function satisfies a Riccati differential equation with polynomial coefficients, in terms of second order matrix differential equations.
- Matrix Sylvester equations in the theory of orthogonal polynomials on the unit circlePublication . Branquinho, A.; Rebocho, M. N.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.