ON SPECTRAL GAPS OF A LAPLACIAN IN A STRIP WITH A BOUNDED PERIODIC PERTURBATION

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

ON SPECTRAL GAPS OF A LAPLACIAN IN A STRIP WITH A BOUNDED PERIODIC PERTURBATION

Popis výsledku v původním jazyce

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 &quot;the maximal oscillation of the perturbation&quot;. 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.

Název v anglickém jazyce

ON SPECTRAL GAPS OF A LAPLACIAN IN A STRIP WITH A BOUNDED PERIODIC PERTURBATION

Popis výsledku anglicky

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 &quot;the maximal oscillation of the perturbation&quot;. 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

UFA MATHEMATICAL JOURNAL

ISSN

2074-1863

e-ISSN

—

Svazek periodika

10

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

RU - Ruská federace

Počet stran výsledku

17

Strana od-do

14-30

Kód UT WoS článku

000438890500002

EID výsledku v databázi Scopus

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