The essential spectrum of the Laplacian

Abstract

In this article we prove a generalization of Weyl's criterion for the essential spectrum of a self-adjoint operator on a Hilbert space. We then apply this criterion to the Laplacian on functions over open manifolds and get new results for its essential spectrum.

Cited by in corpus (2)

• Eigenvalues of the drifted Laplacian on complete metric measure spaces
• Heat kernel estimates and the essential spectrum on weighted manifolds