Article ID Journal Published Year Pages File Type
6415156 Journal of Functional Analysis 2013 23 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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