Dichotomies for triangular systems on Hilbert spaces
Dynamical Systems
2025-08-07 v1 Classical Analysis and ODEs
Abstract
In this article, we study the relationship between the exponential dichotomy properties of a triangular system of linear difference equations and its associated diagonal system on Hilbert spaces. We stress that all previous results in this direction were restricted to the finite-dimensional case. As in the previous work of the first two authors, we rely on the relationship between exponential dichotomies and the so-called admissibility properties. However, this approach requires nontrivial changes when passing from the finite-dimensional to the infinite-dimensional setting.
Cite
@article{arxiv.2508.04320,
title = {Dichotomies for triangular systems on Hilbert spaces},
author = {Davor Dragicevic and Kenneth J. Palmer and Boris Petkovic},
journal= {arXiv preprint arXiv:2508.04320},
year = {2025}
}