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Fractional powers and singular perturbations of quantum differential Hamiltonians

TitleFractional powers and singular perturbations of quantum differential Hamiltonians
Publication TypeJournal Article
Year of Publication2018
AuthorsMichelangeli, A, Ottolini, A, Scandone, R
JournalJournal of Mathematical Physics
Volume59
Pagination072106
Abstract

We consider the fractional powers of singular (point-like) perturbations of the Laplacian and the singular perturbations of fractional powers of the Laplacian, and we compare two such constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schrödinger equations for the corresponding operators, we outline a programme of relevant questions that deserve being investigated.

URLhttps://doi.org/10.1063/1.5033856
DOI10.1063/1.5033856

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