On fractional powers of singular perturbations of the Laplacian

Vladimir Simeonov Gueorguiev, Alessandro Michelangeli, Raffaele Scandone

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    We qualify a relevant range of fractional powers of the so-called Hamiltonian of point interaction in three dimensions, namely the singular perturbation of the negative Laplacian with a contact interaction supported at the origin. In particular we provide an explicit control of the domain of such a fractional operator and of its decomposition into regular and singular parts. We also qualify the norms of the resulting singular fractional Sobolev spaces and their mutual control with the corresponding classical Sobolev norms.

    Original languageEnglish
    JournalJournal of Functional Analysis
    DOIs
    Publication statusAccepted/In press - 2018 Jan 1

    Keywords

    • Point interactions
    • Regular and singular component of a point-interaction operator
    • Singular perturbations of the Laplacian

    ASJC Scopus subject areas

    • Analysis

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