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Matematicheskie Zametki, 2015, Volume 98, Issue 6, Pages 809–823
DOI: https://doi.org/10.4213/mzm10974 (Mi mzm10974) 		 
This article is cited in 3 scientific papers (total in 3 papers)

The Emergence of Eigenvalues of a PT-Symmetric Operator in a Thin Strip

D.I. Borisovabc

a Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center
b Bashkir State Pedagogical University, Ufa
c University of Hradec Králové
Full-text PDF (556 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm10974
Abstract: The Schrödinger operator in a thin infinite strip with PT-symmetric boundary conditions and a localized potential is studied. The case of a virtual level on the threshold of the essential spectrum of an efficient one-dimensional operator is considered. Sufficient conditions for the transformation of this level into an isolated eigenvalue are obtained and the first terms of the asymptotic expansion are calculated for this eigenvalue. Sufficient conditions for the absence of such an eigenvalue are also obtained.
Keywords: elliptic operator, thin infinite strip, PT-symmetric boundary condition, localized potential, isolated eigenvalue, asymptotics.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-97009
Ministry of Education and Science of the Russian Federation МД-183.2014.1
Received: 26.03.2014
English version:
Mathematical Notes, 2015, Volume 98, Issue 6, Pages 872–883
DOI: https://doi.org/10.1134/S000143461511019X
Bibliographic databases:
Document Type: Article
UDC: 517.956+517.958
Language: Russian
Citation: D.I. Borisov, “The Emergence of Eigenvalues of a PT-Symmetric Operator in a Thin Strip”, Mat. Zametki, 98:6 (2015), 809–823; Math. Notes, 98:6 (2015), 872–883
Citation in format AMSBIB
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\pages 809--823
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Linking options:
  • https://www.mathnet.ru/eng/mzm10974
  • https://doi.org/10.4213/mzm10974
  • https://www.mathnet.ru/eng/mzm/v98/i6/p809
    • This publication is cited in the following 3 articles:
    1. Borisov I D., Zezyulin D.A., Znojil M., “Bifurcations of Thresholds in Essential Spectra of Elliptic Operators Under Localized Non-Hermitian Perturbations”, Stud. Appl. Math., 146:4 (2021), 834–880  crossref  mathscinet  isi
    2. Borisov I D., Zezyulin D.A., “Bifurcations of Essential Spectra Generated By a Small Non-Hermitian Hole. i. Meromorphic Continuations”, Russ. J. Math. Phys., 28:4 (2021), 416–433  crossref  mathscinet  isi
    3. D. I. Borisov, M. Znojil, “On eigenvalues of a PT-symmetric operator in a thin layer”, Sb. Math., 208:2 (2017), 173–199  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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