15/9/2020
Speaker: Lino Gustavo Garza Gaona
Title: On Differential Equations Associated with Perturbations of Orthogonal Polynomials on the Unit Circle.
Abstract: In this contribution, we propose an algorithm to compute holonomic second-order differential equations satisfied by some families of orthogonal polynomials. Such an algorithm is based on three properties that orthogonal polynomials satisfy: a recurrence relation, a structure formula, and a connection formula. This approach is used to obtain second-order differential equations whose solutions are orthogonal polynomials associated with some spectral transformations of a measure on the unit circle, as well as orthogonal polynomials associated with coherent pairs of measures on the unit circle.
Categorías