Admissibility for Nonuniform ( μ , ν ) Contraction and Dichotomy

Abstract

The relation between the notions of nonuniform asymptotic stability and admissibility is considered. Using appropriate Lyapunov norms, it is showed that if any of their associated ${ℒ}^p$ spaces, with $p\in (1,\infty ]$, is admissible for a given evolution process, then this process is a nonuniform $(\mu ,\nu )$ contraction and dichotomy. A collection of admissible Banach spaces for any given nonuniform $(\mu ,\nu )$ contraction and dichotomy is provided.