Nonuniform dichotomy spectrum and reducibility for nonautonomous difference equations

TL;DR

This paper introduces the nonuniform dichotomy spectrum for nonautonomous difference equations, establishes a spectral theorem, and demonstrates reducibility via weak kinematical similarity, advancing the understanding of their spectral properties.

Contribution

It defines the nonuniform dichotomy spectrum, proves a spectral theorem, and introduces weak kinematical similarity to achieve reducibility results.

Findings

Defined the nonuniform dichotomy spectrum for difference equations

Proved a spectral theorem for this spectrum

Established reducibility through weak kinematical similarity

Abstract

For nonautonomous linear difference equations, we introduce the notion of the so-called nonuniform dichotomy spectrum and prove a spectral theorem. Moreover, we introduce the notion of weak kinematical similarity and prove a reducibility result by the spectral theorem.