On fractional powers of singular perturbations of the Laplacian
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Date
2017
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Abstract
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.
Description
Partially supported by the 2014-2017 MIUR-FIR grant \Cond-Math: Condensed Matter and
Mathematical Physics" code RBFR13WAET.
Keywords
Point interactions, Singular perturbations of the Laplacian, Regular and singular component of a point-interaction operator