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Enforced stability of a simple eigenvalue in the continuous spectrum of a waveguide. / Nazarov, S. A.

In: Functional Analysis and its Applications, Vol. 47, No. 3, 01.07.2013, p. 195-209.

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Nazarov, S. A. / Enforced stability of a simple eigenvalue in the continuous spectrum of a waveguide. In: Functional Analysis and its Applications. 2013 ; Vol. 47, No. 3. pp. 195-209.

BibTeX

@article{edaf29629c344a5291ae06baaf5d873b,
title = "Enforced stability of a simple eigenvalue in the continuous spectrum of a waveguide",
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, local perturbations of quantum waveguide, perturbation of eigenvalue",
author = "Nazarov, {S. A.}",
year = "2013",
month = jul,
day = "1",
doi = "10.1007/s10688-013-0026-8",
language = "English",
volume = "47",
pages = "195--209",
journal = "Functional Analysis and its Applications",
issn = "0016-2663",
publisher = "Springer Nature",
number = "3",

}

RIS

TY - JOUR

T1 - Enforced stability of a simple eigenvalue in the continuous spectrum of a waveguide

AU - Nazarov, S. A.

PY - 2013/7/1

Y1 - 2013/7/1

N2 - 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.

AB - 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.

KW - continuous spectrum

KW - discrete spectrum

KW - local perturbations of quantum waveguide

KW - perturbation of eigenvalue

UR - http://www.scopus.com/inward/record.url?scp=84884380082&partnerID=8YFLogxK

U2 - 10.1007/s10688-013-0026-8

DO - 10.1007/s10688-013-0026-8

M3 - Article

AN - SCOPUS:84884380082

VL - 47

SP - 195

EP - 209

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 3

ER -

ID: 62107905