On the Point Spectrum of Self-Adjoint Operators That Appears under Singular Perturbations of Finite Rank

• Date: 2003
• Main Authors: Dudkin, M. Ye., Koshmanenko, V. D., Дудкін, М. Є., Кошманенко, В. Д.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2003
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4000
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We discuss purely singular finite-rank perturbations of a self-adjoint operator A in a Hilbert space ℋ. The perturbed operators \(\tilde A\) are defined by the Krein resolvent formula \((\tilde A - z)^{ - 1} = (A - z)^{ - 1} + B_z \) , Im z ≠ 0, where B z are finite-rank operators such that d...