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Maximal Accretive Extensions of Schrödinger Operators on Vector Bundles over Infinite Graphs

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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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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of North Florida, Jacksonville, FL, 32224, USA

    Ognjen Milatovic

  2. Unité mixte de recherche CNRS-UJF 5582, Institut Fourier, Grenoble University, BP 74, 38402, Saint Martin d’Hères Cedex, France

    Françoise Truc

Authors
  1. Ognjen Milatovic
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  2. Françoise Truc
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Correspondence to Ognjen Milatovic.

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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

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