ON SPECTRAL GAPS OF A LAPLACIAN IN A STRIP WITH A BOUNDED PERIODIC PERTURBATION
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F18%3A50014840" target="_blank" >RIV/62690094:18470/18:50014840 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.13108/2018-10-2-14" target="_blank" >http://dx.doi.org/10.13108/2018-10-2-14</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.13108/2018-10-2-14" target="_blank" >10.13108/2018-10-2-14</a>
Alternative languages
Result language
angličtina
Original language name
ON SPECTRAL GAPS OF A LAPLACIAN IN A STRIP WITH A BOUNDED PERIODIC PERTURBATION
Original language description
In the work we consider the Laplacian subject to the Dirichlet condition in an infinite planar strip perturbed by a periodic operator. The perturbation is introduced as an arbitrary bounded periodic operator in L-2 on the periodicity cell; then this operator is extended periodically on the entire strip. We study the band spectrum of such operator. The main obtained result is the absence of the spectral gaps in the lower part of the spectrum for a sufficiently small potential. The upper bound for the period ensuring such result is written explicitly as a certain number. It also involves a certain characteristics of the perturbing operator, which can be nonrigorously described as "the maximal oscillation of the perturbation". We also explicitly write out the length of the part of the spectrum, in which the absence of the gaps is guaranteed. Such result can be regarded as a partial proof of the strong Bethe-Sommerfeld conjecture on absence of internal gaps in the band spectra of periodic operators for sufficiently small periods.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
UFA MATHEMATICAL JOURNAL
ISSN
2074-1863
e-ISSN
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Volume of the periodical
10
Issue of the periodical within the volume
2
Country of publishing house
RU - RUSSIAN FEDERATION
Number of pages
17
Pages from-to
14-30
UT code for WoS article
000438890500002
EID of the result in the Scopus database
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