On an application of the Lax-Phillips scattering approach in the theory of singular perturbations

For a singular perturbation A = A 0 + ∑ i, j = 1 n t 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 G-fraktur sing (AT, A0)(δ) is calculated in terms of parameters t ij under some additional restrictions on singular elements ψ j. The results obtained enable one to apply the Lax-Phillips approach in scattering theory. © 2005 Springer Science+Business Media, Inc.