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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

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

2021

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

496

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

28

Strana od-do

"Article Number: 124809"

Kód UT WoS článku

000600560800016

EID výsledku v databázi Scopus

2-s2.0-85097085712