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  • A Glazman-Povzner-Wienholtz theorem on graphs
    Kostenko, Aleksej Sergejevič, 1980- ; Malamud, Mark Mihajlovič, 1950- ; Nicolussi, Noema
    The Glazman-Povzner-Wienholtz theorem states that the semiboundedness of a Schrödinger operator, when combined with suitable local regularity assumptions on its potential and the completeness of the ... underlying manifold, 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 which are locally ▫$H^{-1}$▫. Moreover, we exploit recently discovered connections between Schrödinger operators on metric graphs and weighted graphs in order to prove a discrete version of the Glazman-Povzner-Wienholtz theorem.
    Source: Advances in mathematics. - ISSN 0001-8708 (Vol. 395, [article no.] 108158, Feb. 2022, 30 str.)
    Type of material - article, component part ; adult, serious
    Publish date - 2022
    Language - english
    COBISS.SI-ID - 171947523

    Link(s):

    https://www.sciencedirect.com/science/article/pii/S0001870821005971
    DOI

source: Advances in mathematics. - ISSN 0001-8708 (Vol. 395, [article no.] 108158, Feb. 2022, 30 str.)

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