Exponential dichotomy and $(L^p,L^q)$-admissibility
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.
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Nonlinear Differential Equations Analysis
Advanced Banach Space Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 10 January 2026
- Document type
- Preprint