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Spectra of definite type in waveguide models
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SYSNO ASEP 0473757 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Spectra of definite type in waveguide models Author(s) Lotoreichik, Vladimir (UJF-V) ORCID, SAI
Siegl, Petr (UJF-V) RIDNumber of authors 2 Source Title Proceedings of the American Mathematical Society. - : American Mathematical Society - ISSN 0002-9939
Roč. 145, č. 3 (2017), s. 1231-1246Number of pages 16 s. Publication form Print - P Language eng - English Country US - United States Keywords spectral points of definite and of type pi ; weakly coupled bound states ; pertrubations of essential spectrum ; PT-symmetric waveguide Subject RIV BE - Theoretical Physics OECD category Applied mathematics R&D Projects GA14-06818S GA ČR - Czech Science Foundation (CSF) Institutional support UJF-V - RVO:61389005 UT WOS 000391660700029 EID SCOPUS 85007295448 DOI 10.1090/proc/13316 Annotation 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. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2018
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