The essential spectrum of the Laplacian

2012/11/14 by Charalambous, Nelia, Lu, Zhiqin
#58E30 #58J50 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1211.3225

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.

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