naa a22 4500 510812546 CHVBK 20180411083449.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1134/S0081543813050027 doi (NATIONALLICENCE)springer-10.1134/S0081543813050027 Borisov D. M.Akmullah Bashkir State Pedagogical University, ul. Oktyabrskoi Revolyutsii 3a, 450000, Ufa, Russia aut On a PT -symmetric waveguide with a pair of small holes [Elektronische Daten] [D. Borisov] A planar PT-symmetric waveguide with a pair of small holes is considered. The waveguide is modeled by a planar infinite strip in which a pair of symmetric small holes is cut out. The operator is the Laplacian with PT-symmetric boundary condition at the edges of the strip and Neumann condition at the boundaries of the holes. For this operator, the uniform resolvent convergence is established and the convergence rate is estimated. The effect of the generation by the holes of new eigenvalues from the boundary of the continuous spectrum is studied. Sufficient conditions for the existence and absence of such eigenvalues are obtained and the first terms of their asymptotic expansions are found. Pleiades Publishing, Ltd., 2013 PT -symmetric waveguide nationallicence small hole nationallicence uniform resolvent convergence nationallicence asymptotics nationallicence Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 281(2013-06-01), 5-21 0081-5438 281<5 2013 281 11501 https://doi.org/10.1134/S0081543813050027 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813050027 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Borisov D. M.Akmullah Bashkir State Pedagogical University, ul. Oktyabrskoi Revolyutsii 3a, 450000, Ufa, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 281(2013-06-01), 5-21 0081-5438 281<5 2013 281 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer