On an Application of the Lax-Phillips Scattering Approach in the Theory of Singular Perturbations - Kuzhel', S. A.; Matsyuk, L. V. (Ukrains’kyi Matematychnyi Zhurnal, 2005)
For a singular perturbation A = A_0 + ^n_i, j=1t_ij ψ_j, · ψ_i,n ≤ ∞ of a positive self-adjoint operator A_0 with Lebesgue spectrum, the spectral analysis of the corresponding self-adjoint operator realizations A_T is carried out and the scattering matrix S_(A_T, A_0)(δ) is calculated in terms of parameters t_ij under some additional restrictions on singular elements ψ_j that provides the possibility of application of the Lax -Phillips approach in the scattering theory.