On the spectrum of convolution operator with a potential

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F23%3A50020479" target="_blank" >RIV/62690094:18470/23:50020479 - isvavai.cz</a>

Výsledek na webu

<a href="https://linkinghub.elsevier.com/retrieve/pii/S0022247X22005820" target="_blank" >https://linkinghub.elsevier.com/retrieve/pii/S0022247X22005820</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2022.126568" target="_blank" >10.1016/j.jmaa.2022.126568</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the spectrum of convolution operator with a potential

Popis výsledku v původním jazyce

This paper focuses on the spectral properties of a bounded self-adjoint operator in L-2(R-d) being the sum of a convolution operator with an integrable convolution kernel and an operator of multiplication by a continuous potential converging to zero at infinity. We study both the essential and the discrete spectra of this operator. It is shown that the essential spectrum of the sum is the union of the essential spectrum of the convolution operator and the image of the potential. We then provide a number of sufficient conditions for the existence of discrete spectrum and obtain lower and upper bounds for the number of discrete eigenvalues. Special attention is paid to the case of operators possessing countably many points of the discrete spectrum. We also compare the spectral properties of the operators considered in this work with those of classical Schrodinger operators. (c) 2022 Elsevier Inc. All rights reserved.

Název v anglickém jazyce

On the spectrum of convolution operator with a potential

Popis výsledku anglicky

This paper focuses on the spectral properties of a bounded self-adjoint operator in L-2(R-d) being the sum of a convolution operator with an integrable convolution kernel and an operator of multiplication by a continuous potential converging to zero at infinity. We study both the essential and the discrete spectra of this operator. It is shown that the essential spectrum of the sum is the union of the essential spectrum of the convolution operator and the image of the potential. We then provide a number of sufficient conditions for the existence of discrete spectrum and obtain lower and upper bounds for the number of discrete eigenvalues. Special attention is paid to the case of operators possessing countably many points of the discrete spectrum. We also compare the spectral properties of the operators considered in this work with those of classical Schrodinger operators. (c) 2022 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

2023

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

1096-0813

Svazek periodika

517

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

"Article Number: 126568"

Kód UT WoS článku

000999834100007

EID výsledku v databázi Scopus

2-s2.0-85135856990