Rank-one singular perturbations with a dual pair of eigenvalues

摘要

We discuss the eigen-values problem for rank one singular perturbations (A) over tilde = A (+) over tilde alpha[.,omega]omega of a self-adjoint unbounded operator A with a gap in its spectrum. We give a constructive description of operators (A) over tilde which possess at least two new eigenvalues, one in the resolvent set and other in the spectrum of A. [References: 21]