International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 10, Pages 625-638

Examples of Friedrichs model operators with a cluster point of eigenvalues

Serguei I. Iakovlev

Departamento de Matemáticas, Universidad Simón Bolívar, Apartado Postal 89000, Caracas 1080-A, Venezuela

Received 26 February 2002

Copyright © 2003 Serguei I. Iakovlev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.