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
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.
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.