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Funktsional. Anal. i Prilozhen., 2013, Volume 47, Issue 3, Pages 87–90 (Mi faa3122)  

This article is cited in 4 scientific papers (total in 4 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

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.

DOI: https://doi.org/10.4213/faa3122

Full text: PDF file (157 kB)
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English version:
Functional Analysis and Its Applications, 2013, 47:3, 238–240

Bibliographic databases:

UDC: 517.956
Received: 29.11.2011

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. 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
    3. Kuchment P., “An overview of periodic elliptic operators”, Bull. Amer. Math. Soc., 53:3 (2016), 343–414  crossref  mathscinet  zmath  isi  elib  scopus
    4. 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
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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