International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 513215 | https://doi.org/10.1155/S0161171203202155

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

Received26 Feb 2002

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.

Copyright © 2003 Hindawi Publishing Corporation. 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.


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