Spectra of definite type in waveguide models
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F17%3A00473757" target="_blank" >RIV/61389005:_____/17:00473757 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1090/proc/13316" target="_blank" >http://dx.doi.org/10.1090/proc/13316</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/proc/13316" target="_blank" >10.1090/proc/13316</a>
Alternative languages
Result language
angličtina
Original language name
Spectra of definite type in waveguide models
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA14-06818S" target="_blank" >GA14-06818S: Rigorous Methods in Quantum Dynamics: Geometry and Magnetic Fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Proceedings of the American Mathematical Society
ISSN
0002-9939
e-ISSN
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Volume of the periodical
145
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
16
Pages from-to
1231-1246
UT code for WoS article
000391660700029
EID of the result in the Scopus database
2-s2.0-85007295448