An uncertainty principle and lower bounds for the Dirichlet Laplacian on graphs

2016/06/23 by Lenz, Daniel, Stollmann, Peter, Stolz, Gunter
#47 #53 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1606.07476

Abstract

We prove a quantitative uncertainty principle at low energies for the Laplacian on fairly general weighted graphs with a uniform explicit control of the constants in terms of geometric quantities. A major step consists in establishing lower bounds for Dirichlet eigenvalues in terms of the geometry.

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