2019
Том 71
№ 9

# On an Application of the Lax-Phillips Scattering Approach in the Theory of Singular Perturbations

Abstract

For a singular perturbation $A = A_0 + \sum^n_{i, j=1}t_{ij} \langle \psi_j, \cdot \rangle \psi_i,\quad n \leq \infty$ 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 $\psi_{j}$ that provides the possibility of application of the Lax -Phillips approach in the scattering theory.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 5, pp 806-816.

Citation Example: Kuzhel' S. A., Matsyuk L. V. On an Application of the Lax-Phillips Scattering Approach in the Theory of Singular Perturbations // Ukr. Mat. Zh. - 2005. - 57, № 5. - pp. 679–688.

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