Triplet extensions I: Semibounded operators in the scale of Hilbert spaces
2009 (English)In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 107, 251-286 p.Article in journal (Refereed) Published
The extension theory for semibounded symmetric operators is generalized by including operators acting in a triplet of Hilbert spaces. We concentrate our attention on the case where the minimal operator is essentially self-adjoint in the basic Hilbert space and construct a family of its self-adjoint extensions inside the triplet. All such extensions can be described by certain boundary conditions, and a natural counterpart of Krein's resolvent formula is obtained.
Place, publisher, year, edition, pages
2009. Vol. 107, 251-286 p.
rank-one perturbations, self-adjoint operators
IdentifiersURN: urn:nbn:se:su:diva-60220DOI: 10.1007/s11854-009-0011-6ISI: 000264843300011OAI: oai:DiVA.org:su-60220DiVA: diva2:434535
authorCount :12011-08-152011-08-112011-08-15Bibliographically approved