On the Koplienko Spectral Shift Function. I. Basics
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On the Koplienko Spectral Shift Function. I. Basics
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| Creator |
Gesztesy, F.
Pushnitski, A. Simon, B. |
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| 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.
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| Date |
2016-09-29T17:30:21Z
2016-09-29T17:30:21Z 2008 |
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| Type |
Article
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| Identifier |
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 http://dspace.nbuv.gov.ua/handle/123456789/106495 |
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| Language |
en
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| Relation |
Журнал математической физики, анализа, геометрии
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| Publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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