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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Bibliographic Details
Published in:Bulletin of mathematical sciences 2024-04, Vol.14 (1)
Main Authors: Marriaga, Misael E., de Salas, Guillermo Vera, Latorre, Marta, Alcázar, Rubén Muñoz
Format: Article
Language:English
Subjects:
Cholesky factorization
Hankel matrices
Orthogonal polynomials
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Summary: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.
ISSN:1664-3607
1664-3615
DOI:10.1142/S1664360723500066