A Glazman–Povzner–Wienholtz theorem on graphs

@article{Kostenko2022AGT,
  title={A Glazman–Povzner–Wienholtz theorem on graphs},
  author={Aleksey Kostenko and Mark Mikhailovich Malamud and Noema Nicolussi},
  journal={Advances in Mathematics},
  year={2022}
}
The Glazman–Povzner–Wienholtz theorem states that the completeness of a manifold, when combined with the semiboundedness of the Schrödinger operator −∆ + q and suitable local regularity assumptions on q, guarantees its essential self-adjointness. Our aim is to extend this result to Schrödinger operators on graphs. We first obtain the corresponding theorem for Schrödinger operators on metric graphs, allowing in particular distributional potentials q ∈ H loc . Moreover, we exploit recently… 
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There are two main notions of a Laplacian operator associated with graphs: discrete graph Laplacians and continuous Laplacians on metric graphs (widely known as quantum graphs). Both objects have a

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