Maximal accretive extensions of Schr\"odinger operators on vector bundles over infinite graphs
Abstract
Given a Hermitian vector bundle over an infinite weighted graph, we define the Laplacian associated to a unitary connection on this bundle and study the essential self-adjointness of a perturbation of this Laplacian by an operator-valued potential. Additionally, we give a sufficient condition for the resulting Schr\"odinger operator to serve as the generator of a strongly continuous contraction semigroup in the corresponding l^{p}-space.
Keywords
Cite
@article{arxiv.1307.1213,
title = {Maximal accretive extensions of Schr\"odinger operators on vector bundles over infinite graphs},
author = {Ognjen Milatovic and Francoise Truc},
journal= {arXiv preprint arXiv:1307.1213},
year = {2014}
}
Comments
We have made significant revisions of the previous version. In particular, this version has a new title: "Maximal Accretive Extensions of Schr\"odinger Operators on Vector Bundles over Infinite Graphs." The final version will appear in Integral Equations and Operator Theory and will be availableat Springer via http://dx.doi.org/10.1007/s00020-014-2196-z