Approximations of the connection Laplacian spectra

被引：1

作者：

Burago, Dmitri ^{[1
]}

Ivanov, Sergei ^{[2
]}

Kurylev, Yaroslav ^{[3
]}

Lu, Jinpeng ^{[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] Univ Helsinki, Dept Math & Stat, Helsinki 00014, Finland

来源：

MATHEMATISCHE ZEITSCHRIFT | 2022年 / 301卷 / 03期

关键词：

Connection Laplacian; Spectral convergence; Discretization; DIFFUSION MAPS;

D O I：

10.1007/s00209-022-03016-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a convolution-type operator on vector bundles over metric-measure spaces. This operator extends the analogous convolution Laplacian on functions in our earlier work to vector bundles, and is a natural extension of the graph connection Laplacian. We prove that for Euclidean or Hermitian connections on closed Riemannian manifolds, the spectrum of this operator and that of the graph connection Laplacian both approximate the spectrum of the connection Laplacian.

引用

页码：3185 / 3206

页数：22

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