A note on self-adjoint extensions of the Laplacian on weighted graphs

Xueping Huang, Matthias Keller, Jun Masamune, Radosław K. Wojciechowski

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)

Abstract

We study the uniqueness of self-adjoint and Markovian extensions of the Laplacian on weighted graphs. We first show that, for locally finite graphs and a certain family of metrics, completeness of the graph implies uniqueness of these extensions. Moreover, in the case when the graph is not metrically complete and the Cauchy boundary has finite capacity, we characterize the uniqueness of the Markovian extensions.

Original languageEnglish
Pages (from-to)1556-1578
Number of pages23
JournalJournal of Functional Analysis
Volume265
Issue number8
DOIs
Publication statusPublished - 2013 Oct 15

Keywords

  • Essential self-adjointness
  • Intrinsic metrics
  • Laplacians
  • Weighted graphs

ASJC Scopus subject areas

  • Analysis

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