Examples of Friedrichs model operators with a cluster point of eigenvalues (Q1864300)

This paper considers a family of selfadjoint operators of the Friedrichs model which are symmetric type operators having one singular point, zero of order \(m\). For every \(m> 3/2\), a rank 1 perturbation is constructed from the class \(\text{Lip\,}1\) such that the corresponding operator has a sequence of eigenvalues converging to zero. Hence for \(m> 3/2\) and near the singular point, there is no singular spectrum finiteness condition in terms of a modulus of continuity of a perturbation for these operators.