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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| Main Author: | |
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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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |