Spectral stability of metric-measure Laplacians

2015/06/22 by Burago, Dmitri, Ivanov, Sergei, Kurylev, Yaroslav · 1 citation
#53C23 #58C40 #65J10 #FOS: Mathematics #Metric Geometry (math.MG) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1506.06781

Abstract

We consider a "convolution mm-Laplacian" operator on metric-measure spaces and study its spectral properties. The definition is based on averaging over small metric balls. For reasonably nice metric-measure spaces we prove stability of convolution Laplacian's spectrum with respect to metric-measure perturbations and obtain Weyl-type estimates on the number of eigenvalues.

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• Stability of Gel'fand's inverse interior spectral problem for Schrödinger operators

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