Factorization for the matrix-valued general Jacobi system on the full-line lattice
Abstract
The Jacobi system with matrix-valued coefficients and with the spectral parameter depending on a matrix-valued weight factor is considered on the full-line lattice. The scattering from the full-line lattice is expressed in terms of the scattering from the fragments of the whole lattice by developing a factorization formula for the corresponding transition matrices. In particular, the matrix-valued transmission and reflection coefficients for the full-line lattice are explicitly expressed in terms of the scattering coefficients for the left and right lattice fragments. Since the matrix-valued scattering coefficients are easier to determine for the fragments than for the full-line lattice, the factorization formula presented provides a method to determine the scattering coefficients for full-line lattices. The theory presented is illustrated with various explicit examples, including an example demonstrating that the matrix-valued left transmission coefficient in general is not equal to the matrix-valued right transmission coefficient for a lattice.
Cite
@article{arxiv.2511.18229,
title = {Factorization for the matrix-valued general Jacobi system on the full-line lattice},
author = {Tuncay Aktosun and Abdon E. Choque-Rivero and Vassilis G. Papanicolaou and Mehmet Unlu and Ricardo Weder},
journal= {arXiv preprint arXiv:2511.18229},
year = {2026}
}