Friday, July 5, 2013

1307.1213 (Ognjen Milatovic et al.)

Essential self-adjointness of Schrödinger operators on vector bundles
over infinite graphs

Ognjen Milatovic, Francoise Truc
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.
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