Sebastian Haeseler, Matthias Keller, Radosław K. Wojciechowski
Published 2012-05-22Version 1
We consider operators arising from regular Dirichlet forms with vanishing killing term. We give bounds for the bottom of the (essential) spectrum in terms of exponential volume growth with respect to an intrinsic metric. As special cases we discuss operators on graphs. When the volume growth is measured in the natural graph distance (which is not an intrinsic metric) we discuss the threshold for positivity of the bottom of the spectrum and finiteness of the bottom of the essential spectrum of the (unbounded) graph Laplacian. This threshold is shown to lie at cubic polynomial growth.
Gohberg lemma, compactness, and essential spectrum of operators on compact Lie groups
The essential spectrum of the Neumann--Poincaré operator on a domain with corners
Limit Operators, Compactness and Essential Spectra on Bounded Symmetric Domains
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