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Funktsional'nyi Analiz i ego Prilozheniya, 2013, Volume 47, Issue 3, Pages 87–90
DOI: https://doi.org/10.4213/faa3122 (Mi faa3122) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Brief communications

On the Extrema of Band Functions in Periodic Waveguides

D.I. Borisovab, K. V. Pankrashinc

a Institute of Mathematics with Computing Center, Russian Academy of Sciences, Ufa
b Bashkir State Pedagogical University, Ufa
c Laboratoire de mathématique, Université Paris-Sud
Full-text PDF (157 kB) Citations (6)
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DOI: https://doi.org/10.4213/faa3122
Abstract: In the work we construct an example of a periodic differential operator whose spectrum has gaps with edges attained by the band functions at interior points of the Brillouin zone. This example is the Laplacian on a pair of infinite parallel strips with common boundary from which a periodic system of small holes is cut out. At that, on the outer boundaries the Dirichlet condition is imposed, while on the common boundary the Neumann condition is considered.
Keywords: periodic operator, Brillouin zone, gap, spectrum, dispersion law, waveguide.
Received: 29.11.2011
English version:
Functional Analysis and Its Applications, 2013, Volume 47, Issue 3, Pages 238–240
DOI: https://doi.org/10.1007/s10688-013-0030-z
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
Citation: D.I. Borisov, K. V. Pankrashin, “On the Extrema of Band Functions in Periodic Waveguides”, Funktsional. Anal. i Prilozhen., 47:3 (2013), 87–90; Funct. Anal. Appl., 47:3 (2013), 238–240
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/faa/v47/i3/p87
    • This publication is cited in the following 6 articles:
    1. Borisov I D., Exner P., “Gap Opening in Two-Dimensional Periodic Systems”, Commun. Contemp. Math., 23:1 (2021), 1950080  crossref  mathscinet  zmath  isi
    2. Kuchment P., “An overview of periodic elliptic operators”, Bull. Amer. Math. Soc., 53:3 (2016), 343–414  crossref  mathscinet  zmath  isi  elib  scopus
    3. Borisov D.I., “Creation of spectral bands for a periodic domain with small windows”, Russ. J. Math. Phys., 23:1 (2016), 19–34  crossref  mathscinet  zmath  isi  elib  scopus
    4. Borisov D.I., “on the Band Spectrum of a Schrodinger Operator in a Periodic System of Domains Coupled By Small Windows”, Russ. J. Math. Phys., 22:2 (2015), 153–160  crossref  mathscinet  zmath  isi  elib  scopus
    5. D. I. Borisov, “Perturbation of Threshold of Essential Spectrum for Waveguides with Windows. II: Asymptotics”, J Math Sci, 210:5 (2015), 590  crossref
    6. Borisov D., Pankrashkin K., “Quantum Waveguides with Small Periodic Perturbations: Gaps and Edges of Brillouin Zones”, J. Phys. A-Math. Theor., 46:23 (2013), 235203  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    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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    References:94
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