Admissibility for Nonuniform (μ,ν)‎ Contraction and Dichotomy

Abstract EN

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 ℒp spaces, with p∈(1,∞], is admissible for a given evolution process, then this process is a nonuniform (μ,ν) contraction and dichotomy.

A collection of admissible Banach spaces for any given nonuniform (μ,ν) contraction and dichotomy is provided.