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.

10aPoint interactions10aRegular and singular component of a point-interaction operator10aSingular perturbations of the Laplacian1 aGeorgiev, Vladimir1 aMichelangeli, Alessandro1 aScandone, Raffaele uhttp://www.sciencedirect.com/science/article/pii/S0022123618301046