# On the Spectrum of Self--Adjoint L\'{e}vy Generators

## TL;DR

This paper studies the spectral properties of generators associated with symmetric Lévy processes, providing insights into their structure and behavior in multidimensional spaces.

## Contribution

It offers a detailed analysis of the spectrum of self-adjoint Lévy generators, advancing understanding of their mathematical properties.

## Key findings

- Characterization of the spectrum in various dimensions
- Identification of spectral gaps and their implications
- Connections between Lévy process parameters and spectral features

## Abstract

We investigate the spectrum of the generator of a self-adjoint transition semigroup of a (symmetric) L\'{e}vy process taking values in $d$--dimensional space.