TY - JOUR T1 - Fractional powers and singular perturbations of quantum differential Hamiltonians JF - Journal of Mathematical Physics Y1 - 2018 A1 - Alessandro Michelangeli A1 - Andrea Ottolini A1 - Raffaele Scandone AB -

We consider the fractional powers of singular (point-like) perturbations of the Laplacian and the singular perturbations of fractional powers of the Laplacian, and we compare two such constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schrödinger equations for the corresponding operators, we outline a programme of relevant questions that deserve being investigated.

VL - 59 UR - https://doi.org/10.1063/1.5033856 ER -