Characterizations of the $(h,k,\mu,\nu)-$Trichotomy for Linear Time-Varying Systems

TL;DR

This paper introduces a new framework called $(h,k,,)-$trichotomy for analyzing noninvertible linear time-varying systems in Hilbert spaces, linking it to existing dichotomy concepts.

Contribution

It provides a characterization of $(h,k,,)-$trichotomy in terms of coupled systems with $(h,,)-$dichotomy, extending the theoretical understanding.

Findings

Characterization of $(h,k,,)-$trichotomy in Hilbert spaces.

Connection between $(h,k,,)-$trichotomy and coupled systems with $(h,,)-$dichotomy.

Framework for analyzing noninvertible linear time-varying systems.

Abstract

The present paper considers a concept of $(h,k,\mu,\nu)-$trichotomy for noninvertible linear time-varying systems in Hilbert spaces. This work provides a characterization for linear time-varying systems that admits a $(h,k,\mu,\nu)-$trichotomy in terms of two coupled systems having a $(h,\mu,\nu)-$dichotomy.