An admissibility approach to nonuniform exponential dichotomies

Backes, Lucas; Dragičević, Davor; Xia, Yonghui

doi:10.1090/proc/17150

An admissibility approach to nonuniform exponential dichotomies
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by Lucas Backes, Davor Dragičević and Yonghui Xia;

Proc. Amer. Math. Soc. 153 (2025), 1687-1699

DOI: https://doi.org/10.1090/proc/17150

Published electronically: February 10, 2025

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Abstract:

Recently, Wu and Xia [Proc. Amer. Math. Soc. 151 (2023), pp. 4389-4403] presented a characterization of nonuniform exponential dichotomy via admissibility for difference equations. They have improved previously known results by removing the use of Lyapunov norms and the assumption of bounded growth of the system. However, they have restricted their attention to the case of finite dimensional and invertible dynamics. In the present work we go one step further and extend their results to the case of possibly noninvertible and infinite dimensional dynamical systems. We emphasize that our method of proof is different and significantly simpler than the one presented in the aforementioned work.

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