Boundary Relations and Generalized Resolvents of Symmetric Operators in Krein Spaces
| dc.contributor.author | Behrndt, Jussi | |
| dc.contributor.author | Kreusler, Hans-Christian | |
| dc.date.accessioned | 2021-12-17T10:06:45Z | |
| dc.date.available | 2021-12-17T10:06:45Z | |
| dc.date.issued | 2006-09-11 | |
| dc.description.abstract | The classical Krein-Naimark formula establishes a one-to-one correspondence between the generalized resolvents of a closed symmetric operator in a Hilbert space and the class of Nevanlinna families in a parameter space. Recently it was shown by V.A. Derkach, S. Hassi, M.M. Malamud and H.S.V. de Snoo that these parameter families can be interpreted as so-called Weyl families of boundary relations, and a new proof of the Krein-Naimark formula in the Hilbert space setting was given with the help of a coupling method. The main objective of this paper is to generalize the notion of boundary relations and their Weyl families to the Krein space case and to proof some variants of the Krein-Naimark formula in an indefinite setting. | en |
| dc.identifier.issn | 2197-8085 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/15578 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-14351 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 510 Mathematik | en |
| dc.subject.other | symmetric operator | en |
| dc.subject.other | self-adjoint extension | en |
| dc.subject.other | Krein-Naimark formula | en |
| dc.subject.other | generalized resolvent | en |
| dc.subject.other | boundary relation | en |
| dc.subject.other | boundary triplet | en |
| dc.subject.other | (locally) definitizable operator | en |
| dc.subject.other | Krein space | en |
| dc.title | Boundary Relations and Generalized Resolvents of Symmetric Operators in Krein Spaces | en |
| dc.type | Research Paper | en |
| dc.type.version | submittedVersion | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |
| tub.series.issuenumber | 2006, 33 | en |
| tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
| tub.subject.msc2000 | 47B50 Operators on spaces with an indefinite metric | en |
| tub.subject.msc2000 | 47A20 Dilations, extensions, compressions | en |
| tub.subject.msc2000 | 47B25 Symmetric and selfadjoint operators | en |
| tub.subject.msc2000 | 46C20 Spaces with indefinite inner product | en |
| tub.subject.msc2000 | 47A06 Linear relations | en |