Abstract
We characterize the existence of an exponential dichotomy for a difference equation with delay in terms of the invertibility of a certain linear operator between quite general admissible spaces. These include all \(\ell ^p\) spaces with \(p\in [1, +\infty ]\) as well as many other Banach spaces. The characterization requires using special norms that involve the delay.
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Acknowledgements
This work was supported by FCT/Portugal through CAMGSD, IST-ID, projects UIDB/04459/2020 and UIDP/04459/2020. The authors have no financial or nonfinancial interests to disclose. All authors contributed equally to the manuscript, and read and approved this final version.
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Barreira, L., Valls, C. Characterizations of Hyperbolicity in Difference Equations with Delay. Results Math 78, 19 (2023). https://doi.org/10.1007/s00025-022-01784-4
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DOI: https://doi.org/10.1007/s00025-022-01784-4