Kreĭn's trace formula and the spectral shift function
Let A,B be two selfadjoint operators whose difference B−A is trace class. Kreĭn proved the existence of a certain function ξ∈L1(ℝ) such that tr[f(B)−f(A)]=∫ℝf′(x)ξ(x)dx for a large set of functions f. We give here a new proof of this result and discuss the class of admissible functions. Our proof is...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201004318 |
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| _version_ | 1832549963030069248 |
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| author | Khristo N. Boyadzhiev |
| author_facet | Khristo N. Boyadzhiev |
| author_sort | Khristo N. Boyadzhiev |
| collection | DOAJ |
| description | Let A,B be two selfadjoint operators whose difference B−A is
trace class. Kreĭn proved the existence of a certain function ξ∈L1(ℝ) such that tr[f(B)−f(A)]=∫ℝf′(x)ξ(x)dx for a large set of functions f. We give here a new proof of this
result and discuss the class of admissible functions. Our proof is
based on the integral representation of harmonic functions on the
upper half plane and also uses the Baker-Campbell-Hausdorff
formula. |
| format | Article |
| id | doaj-art-de675f6b1c7d49fd8737d4fb60289e0d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-de675f6b1c7d49fd8737d4fb60289e0d2025-02-03T06:08:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0125423925210.1155/S0161171201004318Kreĭn's trace formula and the spectral shift functionKhristo N. Boyadzhiev0Department of Mathematics, Ohio Northern University, Ada 45810, Ohio, USALet A,B be two selfadjoint operators whose difference B−A is trace class. Kreĭn proved the existence of a certain function ξ∈L1(ℝ) such that tr[f(B)−f(A)]=∫ℝf′(x)ξ(x)dx for a large set of functions f. We give here a new proof of this result and discuss the class of admissible functions. Our proof is based on the integral representation of harmonic functions on the upper half plane and also uses the Baker-Campbell-Hausdorff formula.http://dx.doi.org/10.1155/S0161171201004318 |
| spellingShingle | Khristo N. Boyadzhiev Kreĭn's trace formula and the spectral shift function International Journal of Mathematics and Mathematical Sciences |
| title | Kreĭn's trace formula and the spectral shift function |
| title_full | Kreĭn's trace formula and the spectral shift function |
| title_fullStr | Kreĭn's trace formula and the spectral shift function |
| title_full_unstemmed | Kreĭn's trace formula and the spectral shift function |
| title_short | Kreĭn's trace formula and the spectral shift function |
| title_sort | krein s trace formula and the spectral shift function |
| url | http://dx.doi.org/10.1155/S0161171201004318 |
| work_keys_str_mv | AT khristonboyadzhiev kreinstraceformulaandthespectralshiftfunction |