On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F21%3A50017889" target="_blank" >RIV/62690094:18470/21:50017889 - isvavai.cz</a>

Result on the web

<a href="https://www.sciencedirect.com/science/article/pii/S0022247X20309720?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022247X20309720?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2020.124809" target="_blank" >10.1016/j.jmaa.2020.124809</a>

Result language

angličtina

Original language name

On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders

Original language description

We consider a general elliptic operator in an infinite multi-dimensional cylinder with several distant perturbations; this operator is obtained by &quot;gluing&quot; several single perturbation operators H-(k), k = 1, ..., n, at large distances. The coefficients of each operator H-(k) are periodic in the outlets of the cylinder; the structure of these periodic parts at different outlets can be different. We consider a point lambda(0) is an element of R in the essential spectrum of the operator with several distant perturbations and assume that this point is not in the essential spectra of middle operators H-(k), k = 2, ..., n - 1, but is an eigenvalue of at least one of H-(k), k = 1, ..., n. Under such assumption we show that the operator with several distant perturbations possesses finitely many resonances in the vicinity of lambda(0). We find the leading terms in asymptotics for these resonances, which turn out to be exponentially small. We also conjecture that the made assumption selects the only case, when the distant perturbations produce finitely many resonances in the vicinity of lambda(0). Namely, as lambda(0) is in the essential spectrum of at least one of operators H-(k), k = 2, ..., n - 1, we do expect that infinitely many resonances emerge in the vicinity of lambda(0). (C) 2020 Elsevier Inc. All rights reserved.

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

10102 - Applied mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2021

Confidentiality

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

Name of the periodical

Journal of mathematical analysis and applications

ISSN

0022-247X

e-ISSN

—

Volume of the periodical

496

Issue of the periodical within the volume

2

Country of publishing house

US - UNITED STATES

Number of pages

28

Pages from-to

"Article Number: 124809"

UT code for WoS article

000600560800016

EID of the result in the Scopus database

2-s2.0-85097085712