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Examples of Friedrichs model operators with a cluster point of eigenvalues

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  • Serguei I. Iakovlev

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 .

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  • Serguei I. Iakovlev, 2003. "Examples of Friedrichs model operators with a cluster point of eigenvalues," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-14, January.
    • Handle: RePEc:hin:jijmms:513215
    DOI: 10.1155/S0161171203202155
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