On classical orthogonal polynomials and the Cholesky factorization of a class of Hankel matrices

Classical moment functionals (Hermite, Laguerre, Jacobi, Bessel) can be characterized as those linear functionals whose moments satisfy a second-order linear recurrence relation. In this work, we use this characterization to link the theory of classical orthogonal polynomials and the study of Hankel...

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Detalhes bibliográficos
Autores: Marriaga, Misael E., Vera de Salas, Guillermo, Latorre, Marta, Muñóz Alcázar, Rubén
Tipo de documento: artigo
Data de publicação:2023
País:España
Recursos:Universidad Rey Juan Carlos
Repositório:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
OAI Identifier:oai:burjcdigital.urjc.es:10115/24081
Acesso em linha:https://hdl.handle.net/10115/24081
Access Level:Acceso aberto
Palavra-chave:orthogonal polynomials
Hankel matrices
Cholesky factorization
Descrição
Resumo:Classical moment functionals (Hermite, Laguerre, Jacobi, Bessel) can be characterized as those linear functionals whose moments satisfy a second-order linear recurrence relation. In this work, we use this characterization to link the theory of classical orthogonal polynomials and the study of Hankel matrices whose entries satisfy a second-order linear recurrence relation. Using the recurrent character of the entries of such Hankel matrices, we give several characterizations of the triangular and diagonal matrices involved in their Cholesky factorization and connect them with a corresponding characterization of classical orthogonal polynomials.