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

Kazuhiro Kuwae, Takashi Shioya

Research output: Contribution to journalArticlepeer-review

82 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 languageEnglish
Pages (from-to)599-673
Number of pages75
JournalCommunications in Analysis and Geometry
Volume11
Issue number4
DOIs
Publication statusPublished - 2003 Sep

ASJC Scopus subject areas

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

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