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

摘要: We discuss purely singular finite-rank perturbations of a self-adjoint operator A in Hilbert space ℋ. The perturbed operators \(\tilde A\) are defined by the Krein resolvent formula \((\tilde - z)^{ 1} = (A + B_z \), Im z ≠ 0, where Bz such that dom ∩ |0}. For an arbitrary system orthonormal vectors \(\{ \psi _i \} _{i 1}^{n < \infty } \) satisfying condition span |ψ i |0} and collection real numbers \({\lambda}_i \in {\mathbb{R}}^1\), we construct solves eigenvalue problem A\psi {\lambda}_i {\psi}_i , 1, \ldots ,n\). prove uniqueness under rank n.