Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415156 | Journal of Functional Analysis | 2013 | 23 Pages |
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
Authors
Xueping Huang, Matthias Keller, Jun Masamune, RadosÅaw K. Wojciechowski,