On the spectrum of isomorphisms defined on the space of smooth functions which are flat at 0

TL;DR

This paper investigates the spectral properties of the derivative operator combined with isomorphic multiplication on the space of smooth functions that are flat at zero, providing insights into its spectrum and Waelbroeck spectrum.

Contribution

It introduces a detailed analysis of the spectrum and Waelbroeck spectrum for this specific operator on flat smooth functions, a topic not extensively explored before.

Findings

Characterization of the spectrum of the operator

Determination of the Waelbroeck spectrum in this context

Insights into the spectral behavior of operators on flat smooth functions

Abstract

In this note we study the spectrum and the Waelbroeck spectrum of the derivative operator composed with isomorphic multiplication oper