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Asymptotics of eigenvalues and eigenfunctions of a thin square Dirichlet lattice with a curved ligament. / Nazarov, S. A. .
в: Mathematical Notes, Том 105, № 4, 2019, стр. 559-579.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Asymptotics of eigenvalues and eigenfunctions of a thin square Dirichlet lattice with a curved ligament
AU - Nazarov, S. A.
N1 - Nazarov, S.A. Math Notes (2019) 105: 559. https://doi.org/10.1134/S0001434619030295
PY - 2019
Y1 - 2019
N2 - —The spectrum of the Dirichlet problem on the planar square lattice of thin quantum waveguides has a band-gap structure with short spectral bands separated by wide spectral gaps. The curving of at least one of the ligaments of the lattice generates points of the discrete spectrum inside gaps. A complete asymptotic series for the eigenvalues and eigenfunctions are constructed and justified; those for the eigenfunctions exhibit a remarkable behavior imitating the rapid decay ofthe trapped modes: the terms of the series have compact supports that expand unboundedly as the number of the term increases.
AB - —The spectrum of the Dirichlet problem on the planar square lattice of thin quantum waveguides has a band-gap structure with short spectral bands separated by wide spectral gaps. The curving of at least one of the ligaments of the lattice generates points of the discrete spectrum inside gaps. A complete asymptotic series for the eigenvalues and eigenfunctions are constructed and justified; those for the eigenfunctions exhibit a remarkable behavior imitating the rapid decay ofthe trapped modes: the terms of the series have compact supports that expand unboundedly as the number of the term increases.
KW - lattice of thin quantum waveguides
KW - perturbation
KW - essential and discrete spectra
KW - gaps
KW - eigenvalues
KW - asymptotic expansion
UR - https://link.springer.com/content/pdf/10.1134/S0001434619030295.pdf
UR - https://link.springer.com/article/10.1134/S0001434619030295
M3 - Article
VL - 105
SP - 559
EP - 579
JO - Mathematical Notes
JF - Mathematical Notes
SN - 0001-4346
IS - 4
ER -
ID: 40974850