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 $A = A_0 + \sum^n_{i, j=1}t_{ij} \langle ψ_j, · \rangle ψ_i,\quad n ≤ ∞$ 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 $\mathfrak{S}_{(A_T, A_0)}(δ)$ 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.