Open Access

On new points of the discrete spectrum under singular perturbations

Abstract

We study the emergence problem of new points in the discrete spectrum under singular perturbations of a positive operator. We start with the sequential approach to construction of additional eigenvalues for perturbed operators, which was produced by V. Koshmanenko on the base of rigged Hilbert spaces methods. Two new observations are established. We show that one can construct a point of the discrete spectrum of any finite multiplicity in a single step. And that the method of rigged Hilbert spaces admits an application to the modified construction of a new point of the discrete spectrum under super-singular perturbations.

Key words: Rigged Hilbert space, $A$-scale, singular quadratic form, super-singular perturbation.

Article Information

 Title On new points of the discrete spectrum under singular perturbations Source Methods Funct. Anal. Topology, Vol. 24 (2018), no. 3, 288-296 Milestones Received 07/06/2018 Copyright The Author(s) 2018 (CC BY-SA)

Authors Information

H. V. Tuhai
National Aviation University, prosp. Kosmonavta Komarova 1, Kyiv, 03058, Ukraine

Citation Example

H. V. Tuhai, On new points of the discrete spectrum under singular perturbations, Methods Funct. Anal. Topology 24 (2018), no. 3, 288-296.

BibTex

@article {MFAT1089,
AUTHOR = {H. V. Tuhai},
TITLE = {On new points of the discrete spectrum under singular
perturbations},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {24},
YEAR = {2018},
NUMBER = {3},
PAGES = {288-296},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=1089},
}

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