Reduced transfer operators for singular difference equations
Mathematical Physics
2022-11-10 v1 math.MP
Abstract
For tridiagonal block Jacobi operators, the standard transfer operator techniques only work if the off-diagonal entries are invertible. Under suitable assumptions on the range and kernel of these off-diagonal operators which assure a homogeneous minimal coupling between the blocks, it is shown how to construct reduced transfer operators that have the usual Krein space unitarity property and also a crucial monotonicity in the energy variable. This allows to extend the results of oscillation theory to such systems.
Cite
@article{arxiv.2211.05029,
title = {Reduced transfer operators for singular difference equations},
author = {Hermann Schulz-Baldes},
journal= {arXiv preprint arXiv:2211.05029},
year = {2022}
}
Comments
to appear in the J. Difference Equations and Applications