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Point-Like Perturbed Fractional Laplacians Through Shrinking Potentials of Finite Range

TitlePoint-Like Perturbed Fractional Laplacians Through Shrinking Potentials of Finite Range
Publication TypeJournal Article
Year of Publication2019
AuthorsMichelangeli, A, Scandone, R
JournalComplex Analysis and Operator Theory
Date PublishedMay
ISSN1661-8262
Abstract

We construct the rank-one, singular (point-like) perturbations of the d-dimensional fractional Laplacian in the physically meaningful norm-resolvent limit of fractional Schrödinger operators with regular potentials centred around the perturbation point and shrinking to a delta-like shape. We analyse both possible regimes, the resonance-driven and the resonance-independent limit, depending on the power of the fractional Laplacian and the spatial dimension. To this aim, we also qualify the notion of zero-energy resonance for Schrödinger operators formed by a fractional Laplacian and a regular potential.

URLhttps://doi.org/10.1007/s11785-019-00927-w
DOI10.1007/s11785-019-00927-w

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