On classical orthogonal polynomials and the Cholesky factorization of a class of Hankel matrices
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2023-04-11
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World Scientific
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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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Misael E. Marriaga, Guillermo Vera de Salas, Marta Latorre, and Rubén Muñoz Alcázar, On classical orthogonal polynomials and the Cholesky factorization of a class of Hankel matrices, Bulletin of Mathematical Sciences (2023)
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