Analytic Continuation of Resolvents of Elliptic Operators in a Multidimensional Cylinder

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50017099" target="_blank" >RIV/62690094:18470/20:50017099 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007%2Fs10958-020-05014-6" target="_blank" >https://link.springer.com/article/10.1007%2Fs10958-020-05014-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10958-020-05014-6" target="_blank" >10.1007/s10958-020-05014-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Analytic Continuation of Resolvents of Elliptic Operators in a Multidimensional Cylinder

Popis výsledku v původním jazyce

We consider the scalar second order elliptic differential operator in a multidimensional cylinder with the Dirichlet boundary condition. The coefficients of the operator are periodic on both outlets of the cylinder and are arbitrary in its finite part. We study a local analytic continuation of the bordered resolvent of the operator from the upper half-plane to the lower one with respect to the spectral parameter in a neighborhood of an interior point of the essential spectrum. It is shown that the size of the neighborhood depends only on geometric properties of the cylinder and the behavior of periodic components of coefficients of the operator. We introduce the notion of a resonance and formulate the corresponding boundary value problems. We describe the behavior of the bordered resolvent with respect to the spectral parameter in the neighborhood of the point of the essential spectrum. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Název v anglickém jazyce

Analytic Continuation of Resolvents of Elliptic Operators in a Multidimensional Cylinder

Popis výsledku anglicky

We consider the scalar second order elliptic differential operator in a multidimensional cylinder with the Dirichlet boundary condition. The coefficients of the operator are periodic on both outlets of the cylinder and are arbitrary in its finite part. We study a local analytic continuation of the bordered resolvent of the operator from the upper half-plane to the lower one with respect to the spectral parameter in a neighborhood of an interior point of the essential spectrum. It is shown that the size of the neighborhood depends only on geometric properties of the cylinder and the behavior of periodic components of coefficients of the operator. We introduce the notion of a resonance and formulate the corresponding boundary value problems. We describe the behavior of the bordered resolvent with respect to the spectral parameter in the neighborhood of the point of the essential spectrum. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Journal of mathematical sciences

ISSN

1072-3374

e-ISSN

—

Svazek periodika

250

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

25

Strana od-do

260-284

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85090378025