Spectral stability of metric-measure Laplacians

被引：9

作者：

Burago, Dmitri ^{[1
]}

Ivanov, Sergei ^{[2
]}

Kurylev, Yaroslav ^{[3
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[2] Russian Acad Sci, Steklov Math Inst, St Petersburg Dept, Fontanka 27, St Petersburg 191023, Russia

[3] UCL, Dept Math, Gower St, London WC1E 6BT, England

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2019年 / 232卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

MEASURE-SPACES; GEOMETRY;

D O I：

10.1007/s11856-019-1865-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：125 / 158

页数：34

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