Krĕin ’ S Trace Formula and the Spectral Shift Function

  title={Krĕin ’ S Trace Formula and the Spectral Shift Function},
  author={Khristo N. Boyadzhiev},
Let A,B be two selfadjoint operators whose difference B −A is trace class. Krĕın 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. 2000 Mathematics Subject Classification. Primary 47A55… CONTINUE READING

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