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- Distributional equation for Laguerre- Hahn functionals on the unit circlePublication . Branquinho, A.; Rebocho, M. N.Let u be a hermitian linear functional defined in the linear space of Laurent polynomials and F its corresponding Carathéodory function. [...]
- 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 [...]
- Second- order differential equations in the Laguerre-Hahn classPublication . Rebocho, Maria das Neves; Branquinho, A.; Paiva, Anabela; Foulquie-Moreno, AnaLaguerre-Hahn families on the real line are characterized in terms of second order differential equations with matrix coefficients for vectors involving the orthogonal polynomials and their associated polynomials, as well as in terms of second order differential equation for the functions of the second kind. Some characterizations of the classical families are derived.
- 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.