Abstract
For a singular perturbation \(A = A_0 + \sum {_{i,j = 1}^n } t_{ij} \left\langle {\psi _j , \cdot } \right\rangle \psi _i ,n \leqslant \infty\), 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 \(\mathfrak{S}(A_T ,A_0 )(\delta )\) 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.
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Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 5, pp. 679–688, May, 2005.
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Kuzhel', S.O., Matsyuk, L.V. On an Application of the Lax-Phillips Scattering Approach in the Theory of Singular Perturbations. Ukr Math J 57, 806–816 (2005). https://doi.org/10.1007/s11253-005-0230-7
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DOI: https://doi.org/10.1007/s11253-005-0230-7