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This article is cited in 10 scientific papers (total in 10 papers)
On eigenvalues of a $\mathscr{P\!T}$-symmetric operator in a thin layer
D. I. Borisovabc, M. Znojild a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa
b Bashkir State Pedagogical University, Ufa
c University of Hradec Králové, Czech Republic
d Nuclear Physics Institute of the Czech Academy of Sciences, Řež, Czech Republic
Abstract:
We consider an elliptic operator with variable coefficients in a thin three-dimensional layer with $\mathscr{P\!T}$-symmetric boundary conditions. We study the effect of the appearance of isolated eigenvalues at the edges of the gaps in the essential spectrum. We obtain sufficient conditions that guarantee that such eigenvalues either exist or are absent near a given edge of a gap. In the case of existence, the first terms in the asymptotic expansion of these emerging eigenvalues are calculated.
Bibliography: 34 titles.
Keywords:
thin domain, $\mathscr{P\!T}$-symmetric operator, edge of a gap, asymptotics, periodic operator.
Received: 05.01.2016 and 21.05.2016
Citation:
D. I. Borisov, M. Znojil, “On eigenvalues of a $\mathscr{P\!T}$-symmetric operator in a thin layer”, Mat. Sb., 208:2 (2017), 3–30; Sb. Math., 208:2 (2017), 173–199
Linking options:
https://www.mathnet.ru/eng/sm8657https://doi.org/10.1070/SM8657 https://www.mathnet.ru/eng/sm/v208/i2/p3
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Abstract page: | 480 | Russian version PDF: | 56 | English version PDF: | 6 | References: | 43 | First page: | 32 |
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