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On fractional powers of singular perturbations of the Laplacian

TitleOn fractional powers of singular perturbations of the Laplacian
Publication TypePreprint
2017
AuthorsGeorgiev, V, Michelangeli, A, Scandone, R
Document NumberSISSA;71/2016/MATE

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.

http://preprints.sissa.it/handle/1963/35293

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