  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.
