Spectra of definite type in waveguide models

0473757 - ÚJF 2018 RIV US eng J - Journal Article
Lotoreichik, Vladimir - Siegl, Petr
Spectra of definite type in waveguide models.
Proceedings of the American Mathematical Society. Roč. 145, č. 3 (2017), s. 1231-1246. ISSN 0002-9939. E-ISSN 1088-6826
R&D Projects: GA ČR(CZ) GA14-06818S
Institutional support: RVO:61389005
Keywords : spectral points of definite and of type pi * weakly coupled bound states * pertrubations of essential spectrum * PT-symmetric waveguide
OECD category: Applied mathematics
Impact factor: 0.707, year: 2017

We develop an abstract method to identify spectral points of definite type in the spectrum of the operator T-1 circle times I-2 + I-1 circle times T-2, applicable in particular for non-self-adjoint waveguide type operators with symmetries. Using the remarkable properties of the spectral points of definite type, we obtain new results on realness of weakly coupled bound states and of low lying essential spectrum in the PT-symmetric waveguide. Moreover, we show that the pseudospectrum has a tame behavior near the low lying essential spectrum and exclude the accumulation of non-real eigenvalues from this part of the essential spectrum. The advantage of our approach is particularly visible when the resolvent of the unperturbed operator cannot be explicitly expressed and most of the mentioned conclusions are extremely hard to prove by direct methods.
Permanent Link: http://hdl.handle.net/11104/0270896