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Funktsional'nyi Analiz i ego Prilozheniya, 2013, Volume 47, Issue 3, Pages 37–53
DOI: https://doi.org/10.4213/faa3117 (Mi faa3117) 		 
This article is cited in 61 scientific papers (total in 61 papers)

Enforced Stability of a Simple Eigenvalue in the Continuous Spectrum of a Waveguide

S. A. Nazarov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences
Full-text PDF (238 kB) Citations (61)
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DOI: https://doi.org/10.4213/faa3117
Abstract: It is shown in the paper that, under several orthogonality and normalization conditions and a proper choice of accessory parameters, a simple eigenvalue lying between thresholds of the continuous spectrum of the Dirichlet problem in a domain with a cylindrical outlet to infinity is not taken out from the spectrum by a small compact perturbation of the Helmholtz operator. The result is obtained by means of an asymptotic analysis of the augmented scattering matrix.
Keywords: continuous spectrum, discrete spectrum, perturbation of eigenvalue, local perturbations of quantum waveguide.
Received: 01.06.2011
English version:
Functional Analysis and Its Applications, 2013, Volume 47, Issue 3, Pages 195–209
DOI: https://doi.org/10.1007/s10688-013-0026-8
Bibliographic databases:
Document Type: Article
UDC: 517.984.46+517.958+531.33
Language: Russian
Citation: S. A. Nazarov, “Enforced Stability of a Simple Eigenvalue in the Continuous Spectrum of a Waveguide”, Funktsional. Anal. i Prilozhen., 47:3 (2013), 37–53; Funct. Anal. Appl., 47:3 (2013), 195–209
Citation in format AMSBIB
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    • This publication is cited in the following 61 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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