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.

On fractional powers of singular perturbations of the Laplacian

Gueorguiev Vladimir;Raffaele Scandone
2018-01-01

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.
2018
Gueorguiev, Vladimir; Alessandro, Michelangeli; Scandone, Raffaele
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/929418
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