Darboux transformation of symmetric Jacobi matrices and Toda lattices

Let J be a symmetric Jacobi matrix associated with some Toda lattice. We find conditions for Jacobi matrix J to admit factorization J = LU (or J = 𝔘𝔏) with L (or 𝔏) and U (or 𝔘) being lower and upper triangular two-diagonal matrices, respectively. In this case, the Darboux transformation of J is the...

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Bibliographic Details

Published in:	Frontiers in Applied Mathematics and Statistics
Main Authors:	Ivan Kovalyov, Oleksandra Levina
Format:	Article
Language:	English
Published:	Frontiers Media S.A. 2024-05-01
Subjects:	Jacobi matrix Darboux transformation orthogonal polynomials moment problem Toda lattice
Online Access:	https://www.frontiersin.org/articles/10.3389/fams.2024.1397374/full