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On fractional powers of singular perturbations of the Laplacian

TitleOn fractional powers of singular perturbations of the Laplacian
Publication TypeJournal Article
Year of Publication2018
AuthorsGeorgiev, V, Michelangeli, A, Scandone, R
JournalJournal of Functional Analysis
Pagination1551 - 1602
KeywordsPoint interactions; Regular and singular component of a point-interaction operator; Singular perturbations of the Laplacian

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.


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