Georgiev, VladimirMichelangeli, AlessandroScandone, Raffaele2017-09-062017-09-062017https://openscience.sissa.it/handle/1963/35293Partially supported by the 2014-2017 MIUR-FIR grant \Cond-Math: Condensed Matter and Mathematical Physics" code RBFR13WAET.We qualify a relevant range of fractional powers of the so-called Hamiltonian of point interaction in three dimensions, namely the singular perturbation of the negative Laplacian with a contact interaction supported at the origin. In particular we provide an explicit control of the domain of such a fractional operator and of its decomposition into regular and singular parts. We also qualify the norms of the resulting singular fractional Sobolev spaces and their mutual control with the corresponding classical Sobolev norms.enPoint interactionsSingular perturbations of the LaplacianRegular and singular component of a point-interaction operatorPreprint71/2016/MATE