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