Spectral properties of general advection operators and weighted translation semigroups

TL;DR

This paper studies the spectral characteristics of weighted shift semigroups linked to abstract transport equations with Lipschitz vector fields, providing insights applicable to collisionless kinetic theory.

Contribution

It introduces a comprehensive analysis of spectral properties for a broad class of weighted shift semigroups in transport equations, expanding understanding in kinetic theory.

Findings

Spectral properties characterized for weighted shift semigroups.

Applications demonstrated in collisionless kinetic theory.

Results applicable to transport equations with no-reentry boundary conditions.

Abstract

We investigate the spectral properties of a class of weighted shift semigroups associated to abstract transport equations with a Lipschitz--continuous vector field with no--reentry boundary conditions. We illustrate our results with various examples taken from collisionless kinetic theory.