Eigenvalues of the reference operator and semiclassical resonances

We prove that the estimate of the number of the eigenvalues in intervals , of the reference operator L^#(h) related to a self-adjoint operator L(h) is equivalent to the estimate of the integral over λ−δ,λ+δ] of the sum of harmonic measures associated to the resonances of L(h) lying in a complex neighborhood Ω of λ>0 and the number of the positive eigenvalues of L(h) in λ−δ,λ+δ]. We apply this result to obtain a Breit-Wigner approximation of the derivative of the spectral shift function near critical energy levels.