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 SchrÃ¶dinger equations for the corresponding operators, we outline a programme of relevant questions that deserve being investigated.

%B Journal of Mathematical Physics %V 59 %P 072106 %G eng %U https://doi.org/10.1063/1.5033856 %R 10.1063/1.5033856