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arXiv · 2601.06534

Exponential dichotomy and $(L^p,L^q)$-admissibility

Trinh Viet Duoc·Nguyen Van Trong
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Abstract

We consider the notion of an exponential dichotomy with respect to a family of norms for an evolutionary family in a Banach space, and we characterize it by the admissibility of the pair $(L^p,L^q)$ for $p,q \in [1,\infty]$ with $p\ge q$. We then use this characterization to establish the robustness of an exponentially dichotomic evolutionary family with respect to a family of norms.

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Trinh Viet Duoc, Nguyen Van Trong. 2026-01-10. Exponential dichotomy and $(L^p,L^q)$-admissibility. https://arxiv.org/abs/2601.06534

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