On Differential Equations Associated with Perturbations of Orthogonal Polynomials on the Unit Circle

Lino G. Garza, Luis E. Garza and Edmundo J. Huertas
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Lino G. Garza: Departamento de Física y Matemáticas, Universidad de Monterrey, San Pedro Garza García, Nuevo León 66238, Mexico
Luis E. Garza: Facultad de Ciencias, Universidad de Colima, Colima 28045, Mexico
Edmundo J. Huertas: Departamento de Física y Matemáticas, Universidad de Alcalá, Alcalá de Henares, Madrid 28801, Spain

Mathematics, 2020, vol. 8, issue 2, 1-19

Abstract: In this contribution, we propose an algorithm to compute holonomic second-order differential equations satisfied by some families of orthogonal polynomials. Such algorithm is based in 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.

Keywords: Orthogonal polynomials on the unit circle; holonomic differential equations; spectral transformations; coherent pairs of measures (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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