Serguei I. Iakovlev, "Examples of Friedrichs model operators with a cluster point of eigenvalues", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 513215, 14 pages, 2003. https://doi.org/10.1155/S0161171203202155
Examples of Friedrichs model operators with a cluster point of eigenvalues
A family of selfadjoint operators of the Friedrichs model is considered. These symmetric type operators have one singular point, zero of order . For every , we construct a rank 1 perturbation from the class 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 .
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