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Spectral stability of metric-measure Laplacians

Burago, D; Ivanov, S; Kurylev, Y; (2015) Spectral stability of metric-measure Laplacians. Green open access

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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.

Type: Working / discussion paper
Title: Spectral stability of metric-measure Laplacians
Open access status: An open access version is available from UCL Discovery
Publisher version: https://arxiv.org/abs/1506.06781v3
Language: English
Keywords: Laplacian, metric-measure space, spectrum, spectral approximation
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1522489
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