Convergence of spectral structures: A functional analytic theory and its applications to spectral geometry

Kazuhiro Kuwae; Takashi Shioya

doi:10.4310/CAG.2003.v11.n4.a1

Convergence of spectral structures: A functional analytic theory and its applications to spectral geometry

Kazuhiro Kuwae, Takashi Shioya

SCI - Mathematics

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

94 Citations (Scopus)

Abstract

We present a functional analytic framework of some natural topologies on a given family of spectral structures on Hilbert spaces, and study convergence of Riemannian manifolds and their spectral structure induced from the Laplacian. We also consider convergence of Alexandrov spaces, locally finite graphs, and metric spaces with Dirichlet forms. Our study covers convergence of noncompact (or incomplete) spaces whose Laplacian has continuous spectrum.

Original language	English
Pages (from-to)	599-673
Number of pages	75
Journal	Communications in Analysis and Geometry
Volume	11
Issue number	4
DOIs	https://doi.org/10.4310/CAG.2003.v11.n4.a1
Publication status	Published - 2003 Sept

ASJC Scopus subject areas

Analysis
Statistics and Probability
Geometry and Topology
Statistics, Probability and Uncertainty

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10.4310/CAG.2003.v11.n4.a1

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Convergence of spectral structures: A functional analytic theory and its applications to spectral geometry

Abstract

ASJC Scopus subject areas

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