Approximations of the connection Laplacian spectra

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 c...

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Veröffentlicht in:	Mathematische Zeitschrift 2022-07, Vol.301 (3), p.3185-3206
Hauptverfasser:	Burago, Dmitri, Ivanov, Sergei, Kurylev, Yaroslav, Lu, Jinpeng
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Sprache:	eng
Schlagworte:	Convolution Mathematics Mathematics and Statistics Operators (mathematics) Riemann manifold
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description	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.
doi_str_mv	10.1007/s00209-022-03016-5
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title	Approximations of the connection Laplacian spectra
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