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 a perturbation of this Laplacian by an operator-valued potential. We give a sufficient condition for the resulting Schrödinger operator to serve as the generator of a strongly continuous contraction semigroup in the corresponding ℓ p-space. Additionally, in the context of ℓ 2-space, we study the essential self-adjointness of the corresponding Schrödinger operator.
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Milatovic, O., Truc, F. Maximal Accretive Extensions of Schrödinger Operators on Vector Bundles over Infinite Graphs. Integr. Equ. Oper. Theory 81, 35–52 (2015). https://doi.org/10.1007/s00020-014-2196-z
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DOI: https://doi.org/10.1007/s00020-014-2196-z