01079nas a2200133   4500008004100000022001400041245009200055210006900147260000800216520062200224100002900846700002300875856004700898       2019                        eng d  a1661-826200aPoint-Like Perturbed Fractional Laplacians Through Shrinking Potentials of Finite Range0 aPointLike Perturbed Fractional Laplacians Through Shrinking Pote  cMay3 a<p>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.</p>1 aMichelangeli, Alessandro1 aScandone, Raffaele  uhttps://doi.org/10.1007/s11785-019-00927-w