Asymptotics of eigenvalues in spectral gaps under regular perturbations of walls of a periodic waveguide. / Nazarov, S. A.
In: Journal of Mathematical Sciences, Vol. 226, No. 4, 2017, p. 402-444.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Asymptotics of eigenvalues in spectral gaps under regular perturbations of walls of a periodic waveguide
AU - Nazarov, S. A.
N1 - Nazarov, S.A. Asymptotics of Eigenvalues in Spectral Gaps Under Regular Perturbations of Walls of a Periodic Waveguide. J Math Sci 226, 402–444 (2017). https://doi.org/10.1007/s10958-017-3542-x
PY - 2017
Y1 - 2017
N2 - We find asymptotic representations of eigenvalues inside gaps of the continuous spectrum of a periodic waveguide with local smooth gently sloped (of depth ε ≪ 1) perturbations of walls. These eigenvalues reach the upper or lower gap edge as ε → +0. We consider several variants of the gap edge structure and obtain conditions guaranteeing the existence or absence of points of the discrete spectrum in small neighborhoods. We calculate the total number of eigenvalues in a gap for small ε. To justify the asymptotic expansions, we use elementary tools of the theory of spectral measure.
AB - We find asymptotic representations of eigenvalues inside gaps of the continuous spectrum of a periodic waveguide with local smooth gently sloped (of depth ε ≪ 1) perturbations of walls. These eigenvalues reach the upper or lower gap edge as ε → +0. We consider several variants of the gap edge structure and obtain conditions guaranteeing the existence or absence of points of the discrete spectrum in small neighborhoods. We calculate the total number of eigenvalues in a gap for small ε. To justify the asymptotic expansions, we use elementary tools of the theory of spectral measure.
UR - https://link.springer.com/article/10.1007/s10958-017-3542-x
M3 - Article
VL - 226
SP - 402
EP - 444
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 4
ER -
ID: 35187652