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

Autor:	Lino G. Garza, Luis E. Garza, Edmundo J. Huertas
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	orthogonal polynomials on the unit circle holonomic differential equations spectral transformations coherent pairs of measures Mathematics QA1-939
Zdroj:	Mathematics, Vol 8, Iss 2, p 246 (2020)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math8020246
Popis:	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.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/858b8845a7694518b67a2f7bac7ec47c Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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