Lower bounds for Dirichlet Laplacians and uncertainty principles

2018/08/13 by Stollmann, Peter, Stolz, Günter · 1 citation
#35PXX #81Q10 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1808.04202

Abstract

We prove lower bounds for the Dirichlet Laplacian on possibly unbounded domains in terms of natural geometric conditions. This is used to derive uncertainty principles for low energy functions of general elliptic second order divergence form operators with not necessarily continuous main part.

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• Sampling and equidistribution theorems for elliptic second order operators, lifting of eigenvalues, and applications

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