On the Koplienko spectral shift function, I. Basics
| dc.creator | Gesztesy, Fritz | |
| dc.creator | Pushnitski, Alexander | |
| dc.creator | Simon, Barry | |
| dc.date | 2007-05-24 | |
| dc.date.accessioned | 2026-07-07T08:03:08Z | |
| dc.date.available | 2026-07-07T08:03:08Z | |
| dc.description | We study the Koplienko Spectral Shift Function (KoSSF), which is distinct from the one of Krein (KrSSF). KoSSF is defined for pairs $A,B$ with $(A-B)\in\calI_2$, the Hilbert-Schmidt operators, while KrSSF is defined for pairs $A,B$ with $(A-B)\in\calI_1$, the trace class operators. We review various aspects of the construction of both KoSSF and KrSSF. Among our new results are: (i) that any positive Riemann integrable function of compact support occurs as a KoSSF; (ii) that there exist $A,B$ with $(A-B)\in\calI_2$ so $\det_2((A-z)(B-z)^{-1})$ does not have nontangential boundary values; (iii) an alternative definition of KoSSF in the unitary case; and (iv) a new proof of the invariance of the a.c. spectrum under $\calI_1$-perturbations that uses the KrSSF. | |
| dc.description | Submitted to the Marchenko and Pastur birthday issue of Journal of Mathematical Physics, Analysis and Geometry | |
| dc.identifier | https://arxiv.org/abs/0705.3629 | |
| dc.identifier | http://arxiv.org/abs/0705.3629 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129468 | |
| dc.subject | Spectral Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | 47A10, 81Q10 (Primary) 34B27, 47A40, 81Uxx (Secondary) | |
| dc.title | On the Koplienko spectral shift function, I. Basics | |
| dc.type | text |