Michelangeli, AlessandroOttolini, AndreaScandone, Raffaele2018-01-292018-01-292018-01https://openscience.sissa.it/handle/1963/35305Dedicated to Gianfausto Dell'Antonio on the occasion of his 85th birthdayWe consider the fractional powers of singular (point-like) perturbations of the Laplacian and the singular perturbations of fractional powers of the Laplacian, and we compare two such constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schrödinger equations for the corresponding operators, we outline a programme of relevant questions that deserve being investigated.enFractional LaplacianSingular perturbations of differential operatorsKrein-Vĭšik-Birman self-adjoint extension theoryPreprint