Eigenvalues of the reference operator and semiclassical resonances

We prove that the estimate of the number of the eigenvalues in intervals [λ−δ,λ+δ], 00 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.