Point-like perturbed fractional Laplacians through shrinking potentials of finite range

Michelangeli, AlessandroScandone, Raffaele2018-03-292018-03-292018-03https://openscience.sissa.it/handle/1963/35313We 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.enFractional LaplacianSingular perturbations of differential operatorsSchrödinger operators with shrinking potentialsZero-energy resonancePoint-like perturbed fractional Laplacians through shrinking potentials of finite rangePreprint