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- A characterization theorem for semi-classical orthogonal polynomials on non-uniform latticesPublication . Rebocho, M. N.; Filipuk, Galina; Chen, Yang; Branquinho, A.It is proved a characterization theorem for semi-classical orthogonal polynomials on non- uniform lattices that states the equivalence between the Pearson equation for the weight and some systems involving the orthogonal polynomials as well as the functions of the second kind. As a consequence, it is deduced the analogue of the so-called compatibility conditions in the ladder operator scheme. The classical orthogonal polynomials on non- uniform lattices are then recovered under such compatibility conditions, through a closed formula for the recurrence relation coefficients.
- Deformed Laguerre-Hahn orthogonal polynomials on the real linePublication . Branquinho, A.; Rebocho, M. N.We study families of orthogonal polynomials on the real line whose Stieltjes functions satisfy a Riccati type differential equation with polynomial coefficients. We derive discrete dynamical systems, obtained as a result of deformations of the recurrence relation coefficients of the orthogonal polynomials related to the above referred Stieltjes functions.
- On the semiclassical character of orthogonal polynomials satisfying structure relationsPublication . Branquinho, A.; Rebocho, M. N.We prove the semiclassical character of some sequences of orthogonal polynomials [...]
- Coherent pairs of linear functionals on the unit circlePublication . Branquinho, A.; Foulquie-Moreno, Ana; Marcellan, Francisco; Rebocho, M. N.In this paper we extend the concept of coherent pairs of measures from the real line to Jordan arcs and curves. [...]
- Difference and differential equations for deformed Laguerre-Hahn orthogonal polynomials on the unit circlePublication . Branquinho, A.; Rebocho, M. N.Sequences of orthogonal polynomials on the unit circle whose Carath´eodory function satisfies a Riccati-type differential equation with polynomial coefficients are studied. We deduce discrete Lax equations which lead to difference equations for the corresponding sequences of reflection parameters, and we analyze the continuous differential equations that arise when deformations through a dependence on a parameter t occur.