On fractional powers of singular perturbations of the Laplacian

Vladimir Georgiev*, Alessandro Michelangeli, Raffaele Scandone

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1551-1602
Number of pages52
JournalJournal of Functional Analysis
Volume275
Issue number6
DOIs
Publication statusPublished - 2018 Sep 15

Keywords

  • Point interactions
  • Regular and singular component of a point-interaction operator
  • Singular perturbations of the Laplacian

ASJC Scopus subject areas

  • Analysis

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