International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 10, Pages 625-638
doi:10.1155/S0161171203202155

Examples of Friedrichs model operators with a cluster point of eigenvalues

Abstract

A family of selfadjoint operators of the Friedrichs model is considered. These symmetric type operators have one singular point, zero of order m. For every m>3/2, we construct a rank 1 perturbation from the class Lip 1 such that the corresponding operator has a sequence of eigenvalues converging to zero. Thus, near the singular point, there is no singular spectrum finiteness condition in terms of a modulus of continuity of a perturbation for these operators in case of m>3/2.