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...
| Autores: | , , , |
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| 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 |
| 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. |
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