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Mat. Zametki, 2015, Volume 98, Issue 6, Pages 809–823 (Mi mz10974)  

This article is cited in 1 scientific paper (total in 1 paper)

The Emergence of Eigenvalues of a $\mathcal{PT}$-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

Abstract: The Schrödinger operator in a thin infinite strip with $\mathcal{PT}$-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, $\mathcal{PT}$-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


DOI: https://doi.org/10.4213/mzm10974

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English version:
Mathematical Notes, 2015, 98:6, 872–883

Bibliographic databases:

UDC: 517.956+517.958
Received: 26.03.2014

Citation: D.I. Borisov, “The Emergence of Eigenvalues of a $\mathcal{PT}$-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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  • https://doi.org/10.4213/mzm10974
  • http://mi.mathnet.ru/eng/mz/v98/i6/p809

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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. D. I. Borisov, M. Znojil, “On eigenvalues of a $\mathscr{PT}$-symmetric operator in a thin layer”, Sb. Math., 208:2 (2017), 173–199  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математические заметки Mathematical Notes
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