TY - JOUR
T1 - On fractional powers of singular perturbations of the Laplacian
AU - Georgiev, Vladimir
AU - Michelangeli, Alessandro
AU - Scandone, Raffaele
N1 - Funding Information:
Partially supported by the 2014–2017 MIUR-FIR grant “Cond-Math: Condensed Matter and Mathematical Physics” code RBFR13WAET. The first author was supported in part by INdAM, GNAMPA – Gruppo Nazionale per l'Analisi Matematica, la Probabilita e le loro Applicazioni, by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and by Top Global University Project, Waseda University.
Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2018/9/15
Y1 - 2018/9/15
N2 - 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.
AB - 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.
KW - Point interactions
KW - Regular and singular component of a point-interaction operator
KW - Singular perturbations of the Laplacian
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U2 - 10.1016/j.jfa.2018.03.007
DO - 10.1016/j.jfa.2018.03.007
M3 - Article
AN - SCOPUS:85043538987
SN - 0022-1236
VL - 275
SP - 1551
EP - 1602
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 6
ER -