On eigenvalues of a PT-symmetric operator in a thin layer

0475682 - ÚJF 2018 RIV GB eng J - Článek v odborném periodiku
Borisov, D. I. - Znojil, Miloslav
On eigenvalues of a PT-symmetric operator in a thin layer.
Sbornik Mathematics. Roč. 208, č. 2 (2017), s. 173-199. ISSN 1064-5616. E-ISSN 1468-4802
Grant CEP: GA ČR GA16-22945S
Institucionální podpora: RVO:61389005
Klíčová slova: thin domain * pT-symmetric operator * edge of a gap * asymptotics * periodic operator
Obor OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impakt faktor: 0.865, rok: 2017

We consider an elliptic operator with variable coefficients in a thin three-dimensional layer with PT-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.
Trvalý link: http://hdl.handle.net/11104/0272338