Essential self-adjointness for combinatorial Schr\"odinger operators II- Metrically non complete graphs
Spectral Theory
2013-03-05 v3
Abstract
We consider weighted graphs, we equip them with a metric structure given by a weighted distance, and we discuss essential self-adjointness for weighted graph Laplacians and Schr\"odinger operators in the metrically non complete case.
Keywords
Cite
@article{arxiv.1006.5778,
title = {Essential self-adjointness for combinatorial Schr\"odinger operators II- Metrically non complete graphs},
author = {Yves Colin De Verdière and Nabila Torki-Hamza and Francoise Truc},
journal= {arXiv preprint arXiv:1006.5778},
year = {2013}
}
Comments
Revisited version: Ognjen Milatovic wrote to us that he had discovered a gap in the proof of theorem 4.2 of our paper. As a consequence we propose to make an additional assumption (regularity property of the graph) to this theorem. A new subsection (4.1) is devoted to the study of this property and some details have been changed in the proof of theorem 4.2