Kreĭn's trace formula and the spectral shift function
2001 ◽
Vol 25
(4)
◽
pp. 239-252
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Keyword(s):
LetA,Bbe two selfadjoint operators whose differenceB−Ais trace class. Kreĭn proved the existence of a certain functionξ∈L1(ℝ)such thattr[f(B)−f(A)]=∫ℝf′(x)ξ(x)dxfor a large set of functionsf. 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.
2011 ◽
Vol 227
(1)
◽
pp. 319-420
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Keyword(s):
2007 ◽
Vol 19
(10)
◽
pp. 1071-1115
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1996 ◽
Vol 24
(3)
◽
pp. 285-297
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1987 ◽
pp. 74-83
Keyword(s):