Bethe-Sommerfeld conjecture for periodic Schrodinger operators in strip
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F19%3A50016101" target="_blank" >RIV/62690094:18470/19:50016101 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0022247X19305001/pdfft?md5=79abbdba9fe82e988c9222674e6b420f&pid=1-s2.0-S0022247X19305001-main.pdf" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022247X19305001/pdfft?md5=79abbdba9fe82e988c9222674e6b420f&pid=1-s2.0-S0022247X19305001-main.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2019.06.026" target="_blank" >10.1016/j.jmaa.2019.06.026</a>
Alternative languages
Result language
angličtina
Original language name
Bethe-Sommerfeld conjecture for periodic Schrodinger operators in strip
Original language description
We consider the Dirichlet Laplacian in a straight planar strip perturbed by a bounded periodic symmetric operator. We prove the classical Bethe-Sommerfeld conjecture for this operator ; namely, that this operator has finitely many gaps in its spectrum provided a certain special function written as a series satisfies some lower bound. We show that this is indeed the case if the ratio of the period and the width of strip is less than a certain explicit number, which is approximately equal to 0.10121. We also find explicitly the point in the spectrum, above which there is no internal gaps. We then study the case of a sufficiently small period and we prove that in such case the considered operator has no internal gaps in the spectrum. The conditions ensuring the absence are written as certain explicit inequalities.
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
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of mathematical analysis and applications
ISSN
0022-247X
e-ISSN
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Volume of the periodical
479
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
23
Pages from-to
260-282
UT code for WoS article
000480510700012
EID of the result in the Scopus database
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