TY - JOUR T1 - On fractional powers of singular perturbations of the Laplacian JF - Journal of Functional Analysis Y1 - 2018 A1 - Vladimir Georgiev A1 - Alessandro Michelangeli A1 - Raffaele Scandone KW - Point interactions KW - Regular and singular component of a point-interaction operator KW - Singular perturbations of the Laplacian AB -

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.

VL - 275 UR - http://www.sciencedirect.com/science/article/pii/S0022123618301046 ER -