Research output: Contribution to journal › Article › peer-review
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.Research output: Contribution to journal › Article › peer-review
}
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