Admissible Banach function spaces for linear dynamics with nonuniform behavior on the half-line

TL;DR

This paper introduces a new class of Banach function spaces tailored for nonuniform linear dynamics on the half-line, characterizing stability via generator invertibility, applicable to bounded operator differential equations with finite Lyapunov exponents.

Contribution

It defines admissible Banach spaces for nonuniform evolution families and characterizes stability through generator invertibility, extending analysis to bounded operator differential equations.

Findings

Characterization of nonuniform exponential stability via generator invertibility

Introduction of nonuniform evolution semigroups on new Banach spaces

Applicability to all bounded operator differential equations with finite Lyapunov exponent

Abstract

For nonuniform exponentially bounded evolution families on the half-line we introduce a class of Banach function spaces on which we define nonuniform evolution semigroups. We completely characterize nonuniform exponential stability in terms of invertibility of the corresponding generators. We emphasize that in particular our results apply to all linear differential equations with bounded operator and finite Lyapunov exponent.