TY - RPRT
T1 - On fractional powers of singular perturbations of the Laplacian
Y1 - 2017
A1 - Vladimir Georgiev
A1 - Alessandro Michelangeli
A1 - Raffaele Scandone
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, when applicable, of the 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.
UR - http://preprints.sissa.it/handle/1963/35293
N1 - Partially supported by the 2014-2017 MIUR-FIR grant \Cond-Math: Condensed Matter and
Mathematical Physics" code RBFR13WAET.
U1 - 35599
U2 - Mathematics
ER -