On the unitary equivalence of absolutely continuous parts of self-adjoint extensions : dedicated to the memory of M. S. Birman
dc.bibliographicCitation.volume | 1427 | |
dc.contributor.author | Malamud, Mark M. | |
dc.contributor.author | Neidhardt, Hagen | |
dc.contributor.author | Birman, M.S. | |
dc.date.accessioned | 2016-03-24T17:38:28Z | |
dc.date.available | 2019-06-28T08:04:00Z | |
dc.date.issued | 2009 | |
dc.description.abstract | The classical Weyl-von Neumann theorem states that for any self-adjoint operator $A$ in a separable Hilbert space $gotH$ there exists a (non-unique) Hilbert-Schmidt operator $C = C^*$ such that the perturbed operator $A+C$ has purely point spectrum. We are interesting whether this result remains valid for non-additive perturbations by considering self-adjoint extensions of a given densely defined symmetric operator $A$ in $mathfrak H$ and fixing an extension $A_0 = A_0^*$. We show that for a wide class of symmetric operators the absolutely continuous parts of extensions $widetilde A = widetilde A^*$ and $A_0$ are unitarily equivalent provided that their resolvent difference is a compact operator. Namely, we show that this is true whenever the Weyl function $M(cdot)$ of a pair $A,A_0$ admits bounded limits $M(t) := wlim_yto+0M(t+iy)$ for a.e. $t in mathbbR$. This result is applied to direct sums of symmetric operators and Sturm-Liouville operators with operator potentials. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 0946-8633 | |
dc.identifier.uri | https://doi.org/10.34657/2913 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/2130 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.ispartofseries | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik, Volume 1427, ISSN 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject | Symmetric opterators | eng |
dc.subject | self-adjoint extensions | eng |
dc.subject | boundary triplets | eng |
dc.subject | Wels functions | eng |
dc.subject | spectral multiplicity | eng |
dc.subject | unitary equivalence | eng |
dc.subject | direct sums of symmetric operators | eng |
dc.subject | Sturm-Liouville operators with operator potentials | eng |
dc.subject.ddc | 510 | eng |
dc.title | On the unitary equivalence of absolutely continuous parts of self-adjoint extensions : dedicated to the memory of M. S. Birman | eng |
dc.type | report | eng |
dc.type | Text | eng |
dcterms.bibliographicCitation.journalTitle | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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