Gaps in the Spectrum of the Laplacian in a Strip with Periodic Delta Interaction

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F19%3A50016100" target="_blank" >RIV/62690094:18470/19:50016100 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/content/pdf/10.1134%2FS0081543819040047.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1134%2FS0081543819040047.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1134/S0081543819040047" target="_blank" >10.1134/S0081543819040047</a>

Result language

angličtina

Original language name

Gaps in the Spectrum of the Laplacian in a Strip with Periodic Delta Interaction

Original language description

We consider the Laplace operator in an infinite planar strip with a periodic delta interaction. The width of the strip is fixed and for simplicity is chosen equal to pi. The delta interaction is introduced on a periodic system of curves. Each curve consists of a finite number of segments, each having smoothness C-1. The curves are supposed to be strictly internal and do not intersect the boundaries of the strip. The period of their location is 2 epsilon pi, where epsilon is a sufficiently small number. The function describing the delta interaction is also periodic on the system of curves and is assumed to be bounded and measurable. The main result is the following fact. If epsilon &lt;= epsilon(0), where epsilon(0) is a certain explicitly calculated number and the norm of the function describing the delta interaction is smaller than some explicit constant, then the lower part of the spectrum of the operator has no internal gaps. The lower part is understood as the band of the spectrum until some point, which is explicitly calculated in terms of the parameter epsilon as a rather simple function. This result can be considered as a first step to the proof of the strong Bethe-Sommerfeld conjecture on the complete absence of gaps in the spectrum of an operator for a sufficiently small period of location of delta interactions.

Czech name

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Czech description

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Type

J_imp - 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

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2019

Confidentiality

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

Name of the periodical

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS

ISSN

0081-5438

e-ISSN

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Volume of the periodical

305

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

8

Pages from-to

"S16"-"S23"

UT code for WoS article

000491519000004

EID of the result in the Scopus database

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