Bethe-Sommerfeld conjecture for periodic Schrodinger operators in strip

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Bethe-Sommerfeld conjecture for periodic Schrodinger operators in strip

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Bethe-Sommerfeld conjecture for periodic Schrodinger operators in strip

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Journal of mathematical analysis and applications

ISSN

0022-247X

e-ISSN

—

Svazek periodika

479

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

23

Strana od-do

260-282

Kód UT WoS článku

000480510700012

EID výsledku v databázi Scopus

—