Spectral stability of metric-measure Laplacians

Dmitri Burago; Sergei Ivanov; Yaroslav Kurylev

doi:10.1007/s11856-019-1865-7

Spectral stability of metric-measure Laplacians

Dmitri Burago, Sergei Ivanov, Yaroslav Kurylev

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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.

Original language	English (US)
Pages (from-to)	125-158
Number of pages	34
Journal	Israel Journal of Mathematics
Volume	232
Issue number	1
DOIs	https://doi.org/10.1007/s11856-019-1865-7
State	Published - Aug 1 2019

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11856-019-1865-7

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title = "Spectral stability of metric-measure Laplacians",

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{\textquoteright}s spectrum with respect to metric-measure perturbations and obtain Weyl-type estimates on the number of eigenvalues.",

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AU - Ivanov, Sergei

AU - Kurylev, Yaroslav

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N2 - 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.

AB - 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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Spectral stability of metric-measure Laplacians

Abstract

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