On classical orthogonal polynomials and the Cholesky factorization of a class of Hankel matrices
Classical Analysis and ODEs
2023-02-24 v1 Commutative Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.2302.12035,
title = {On classical orthogonal polynomials and the Cholesky factorization of a class of Hankel matrices},
author = {Misael E. Marriaga and Guillermo Vera de Salas and Marta Latorre and Rubén Muñoz Alcázar},
journal= {arXiv preprint arXiv:2302.12035},
year = {2023}
}