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

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

研究成果: Article査読

49 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)1556-1578
ページ数23
ジャーナルJournal of Functional Analysis
265
8
DOI
出版ステータスPublished - 2013 10 15

ASJC Scopus subject areas

  • 分析

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