Absolutely continuous and singular spectral shift functions
Given a self-adjoint operator H₀, a self-adjoint trace-class operator V and a fixed Hilbert-Schmidt operator F with trivial kernel and cokernel, using the limiting absorption principle an explicit set Λ(H₀;F) ⊂ ℝ of full Lebesgue measure is defined, such that for all λ ∈ Λ(H₀+rV;F) ∩ Λ(H₀;F), where r ∈ ℝ, the wave and the scattering matrices S(λ;H₀+rV,H₀) can be defined unambiguously. Many well-known properties of the wave and scattering matrices and operators are proved, including the stationary...