@article {Michelangeli2019, title = {Point-Like Perturbed Fractional Laplacians Through Shrinking Potentials of Finite Range}, journal = {Complex Analysis and Operator Theory}, year = {2019}, month = {May}, 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 Schr{\"o}dinger 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 Schr{\"o}dinger operators formed by a fractional Laplacian and a regular potential.

}, issn = {1661-8262}, doi = {10.1007/s11785-019-00927-w}, url = {https://doi.org/10.1007/s11785-019-00927-w}, author = {Alessandro Michelangeli and Raffaele Scandone} }