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

• Date: 2005
• Main Authors: Kuzhel', S. A., Matsyuk, L. V., Кужіль, С. О., Мацюк, Л. В.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2005
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3634
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 scatteri...