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arXiv · 2508.04320

Dichotomies for triangular systems on Hilbert spaces

Davor Dragicevic·Kenneth J. Palmer·Boris Petkovic
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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.

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Davor Dragicevic, Kenneth J. Palmer, Boris Petkovic. 2025-08-06. Dichotomies for triangular systems on Hilbert spaces. https://arxiv.org/abs/2508.04320

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