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Darboux transformation of symmetric Jacobi matrices and Toda lattices.
- Source :
- Frontiers in Applied Mathematics & Statistics; 2024, p1-9, 9p
- Publication Year :
- 2024
-
Abstract
- 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 = il£) with L (or £) and U ( or il) being lower and upper triangular two-diagonal matrices, respectively. In this case, the Darboux transformation of J is the symmetric Jacobi matrix J^' = UL (or = £il), which is associated with another Toda lattice. In addition, we found explicit transformation formulas for orthogonal polynomials, m-functions and Toda lattices associated with the Jacobi matrices and their Darboux transformations. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 22974687
- Database :
- Complementary Index
- Journal :
- Frontiers in Applied Mathematics & Statistics
- Publication Type :
- Academic Journal
- Accession number :
- 177643154
- Full Text :
- https://doi.org/10.3389/fams.2024.1397374