Maximal accretive extensions of Schrödinger 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 Schrödinger operator to serve as the generator of a strongly continuous contraction semigroup in the corresponding l^{p}-space.
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Submitted on : Sunday, November 9, 2014 - 10:19:52 AM
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Ognjen Milatovic, Francoise Truc. Maximal accretive extensions of Schrödinger operators on vector bundles over infinite graphs. Integral Equations and Operator Theory, Springer Verlag, 2015, 81 (1), pp.35-52. ⟨10.1007/s00020-014-2196-z⟩. ⟨hal-00840850v2⟩

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