# Spectral analysis for convolution operators on locally compact groups

## TL;DR

This paper investigates the spectral properties of convolution operators on locally compact groups, providing a characterization of their spectrum through auxiliary operators and commutator methods.

## Contribution

It introduces a novel approach to analyze the spectrum of convolution operators using auxiliary operators and commutator techniques.

## Key findings

- Characterization of the spectrum of convolution operators.
- Construction of auxiliary operators for pure point and singular subspaces.
- Application of commutator methods in spectral analysis.

## Abstract

We consider operators $H_\mu$ of convolution with measures $\mu$ on locally compact groups. We characterize the spectrum of $H_\mu$ by constructing auxiliary operators whose kernel contain the pure point and singular subspaces of $H_\mu$, respectively. The proofs rely on commutator methods.