Spectrum of Weighted Composition Operators Part IV: Spectrum and essential spectra of weighted composition operators in spaces of smooth functions on $[0,1]$

TL;DR

This paper characterizes the spectrum and essential spectra of invertible weighted composition operators on spaces of smooth functions over the interval [0,1], advancing understanding of their spectral properties.

Contribution

It offers a detailed description of the spectrum and essential spectra for a class of weighted composition operators in smooth function spaces, extending previous spectral analysis results.

Findings

Spectrum and essential spectra are explicitly characterized.

Results apply to invertible operators in smooth function algebras.

Provides new insights into spectral behavior of weighted composition operators.

Abstract

We provide a description of the spectrum and essential spectra of invertible weighted composition operators acting in some algebras of smooth functions on the interval.