Spectral analysis for convolution operators on locally compact groups

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.

arXiv comment14 pages

References in corpus (1)

• Spectral computations on lamplighter groups and Diestel-Leader graphs