On point spectra of vector fields

TL;DR

This paper investigates the point spectra of vector fields, defining their properties and demonstrating their behavior under isometries and for compactly supported cases, revealing trivial spectra in certain conditions.

Contribution

It introduces a formal definition of the point spectrum for vector fields and analyzes its properties, including invariance under isometries and triviality for compactly supported fields.

Findings

Point spectra are well-behaved under isometries.

Point spectra of compactly supported vector fields are trivial.

Provides foundational properties of vector field spectra.

Abstract

The aim of this paper is to investigate the point spectra of vector fields. We will define the point spectrum of a vector field and study some of its basic properties. In particular, we will prove that point spectra are well-behaved under the action of isometries and that the point spectra of compactly supported vector fields are trivial.