On the Koplienko Spectral Shift Function. I. Basics
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) is in I₂, the Hilbert{Schmidt operators, while KrSSF is defined for pairs A,B with (A - B) is in I₁, the trace class operators. We review various aspec...
Gespeichert in:
| Veröffentlicht in: | Журнал математической физики, анализа, геометрии |
|---|---|
| Datum: | 2008 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2008
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/106495 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On the Koplienko Spectral Shift Function. I. Basics / F. Gesztesy, A. Pushnitski, B. Simon // Журнал математической физики, анализа, геометрии. — 2008. — Т. 4, № 1. — С. 63-107. — Бібліогр.: 71 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862732854553739264 |
|---|---|
| author | Gesztesy, F. Pushnitski, A. Simon, B. |
| author_facet | Gesztesy, F. Pushnitski, A. Simon, B. |
| citation_txt | On the Koplienko Spectral Shift Function. I. Basics / F. Gesztesy, A. Pushnitski, B. Simon // Журнал математической физики, анализа, геометрии. — 2008. — Т. 4, № 1. — С. 63-107. — Бібліогр.: 71 назв. — англ. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| 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) is in I₂, the Hilbert{Schmidt operators, while KrSSF is defined for pairs A,B with (A - B) is in I₁, 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) is in I₂ so det₂((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 I₁-perturbations that uses the KrSSF.
|
| first_indexed | 2025-12-07T19:34:21Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-106495 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T19:34:21Z |
| publishDate | 2008 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Gesztesy, F. Pushnitski, A. Simon, B. 2016-09-29T17:30:21Z 2016-09-29T17:30:21Z 2008 On the Koplienko Spectral Shift Function. I. Basics / F. Gesztesy, A. Pushnitski, B. Simon // Журнал математической физики, анализа, геометрии. — 2008. — Т. 4, № 1. — С. 63-107. — Бібліогр.: 71 назв. — англ. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/106495 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) is in I₂, the Hilbert{Schmidt operators, while KrSSF is defined for pairs A,B with (A - B) is in I₁, 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) is in I₂ so det₂((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 I₁-perturbations that uses the KrSSF. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии On the Koplienko Spectral Shift Function. I. Basics Article published earlier |
| spellingShingle | On the Koplienko Spectral Shift Function. I. Basics Gesztesy, F. Pushnitski, A. Simon, B. |
| title | On the Koplienko Spectral Shift Function. I. Basics |
| title_full | On the Koplienko Spectral Shift Function. I. Basics |
| title_fullStr | On the Koplienko Spectral Shift Function. I. Basics |
| title_full_unstemmed | On the Koplienko Spectral Shift Function. I. Basics |
| title_short | On the Koplienko Spectral Shift Function. I. Basics |
| title_sort | on the koplienko spectral shift function. i. basics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106495 |
| work_keys_str_mv | AT gesztesyf onthekoplienkospectralshiftfunctionibasics AT pushnitskia onthekoplienkospectralshiftfunctionibasics AT simonb onthekoplienkospectralshiftfunctionibasics |