01226nas a2200193 4500008004100000022001400041245006800055210006500123300001600188490000800204520054000212653002300752653006700775653004400842100002300886700002900909700002300938856007100961 2018 eng d a0022-123600aOn fractional powers of singular perturbations of the Laplacian0 afractional powers of singular perturbations of the Laplacian a1551 - 16020 v2753 a
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.
10aPoint interactions10aRegular and singular component of a point-interaction operator10aSingular perturbations of the Laplacian1 aGeorgiev, Vladimir1 aMichelangeli, Alessandro1 aScandone, Raffaele uhttp://www.sciencedirect.com/science/article/pii/S0022123618301046