Resonances of 4th order differential operators

Результат исследований: Научные публикации в периодических изданияхстатьянаучнаярецензирование

1 цитирование (Scopus)

Выдержка

We consider fourth order ordinary differential operator with compactly supported coefficients on the line. We define resonances as zeros of the Fredholm determinant which is analytic on a four sheeted Riemann surface. We determine estimates of the number of resonances in complex discs at large radius. We consider resonances of an Euler-Bernoulli operator on the real line with the positive coefficients which are constants outside some finite interval. We show that the Euler-Bernoulli operator has no eigenvalues and resonances iff the positive coefficients are constants on the whole axis.

Язык оригиналаанглийский
Страницы (с-по)137-177
Число страниц41
ЖурналAsymptotic Analysis
Том111
Номер выпуска3-4
DOI
СостояниеОпубликовано - 1 янв 2019

Предметные области Scopus

  • Математика (все)

Цитировать

@article{fd8ec17bd2bc43dfad22eaf880c736b5,
title = "Resonances of 4th order differential operators",
abstract = "We consider fourth order ordinary differential operator with compactly supported coefficients on the line. We define resonances as zeros of the Fredholm determinant which is analytic on a four sheeted Riemann surface. We determine estimates of the number of resonances in complex discs at large radius. We consider resonances of an Euler-Bernoulli operator on the real line with the positive coefficients which are constants outside some finite interval. We show that the Euler-Bernoulli operator has no eigenvalues and resonances iff the positive coefficients are constants on the whole axis.",
keywords = "Fourth order operators, resonances, scattering, trace formula",
author = "Andrey Badanin and Korotyaev, {Evgeny L.}",
year = "2019",
month = "1",
day = "1",
doi = "10.3233/ASY-181489",
language = "English",
volume = "111",
pages = "137--177",
journal = "Asymptotic Analysis",
issn = "0921-7134",
publisher = "IOS Press",
number = "3-4",

}

Resonances of 4th order differential operators. / Badanin, Andrey; Korotyaev, Evgeny L.

В: Asymptotic Analysis, Том 111, № 3-4, 01.01.2019, стр. 137-177.

Результат исследований: Научные публикации в периодических изданияхстатьянаучнаярецензирование

TY - JOUR

T1 - Resonances of 4th order differential operators

AU - Badanin, Andrey

AU - Korotyaev, Evgeny L.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We consider fourth order ordinary differential operator with compactly supported coefficients on the line. We define resonances as zeros of the Fredholm determinant which is analytic on a four sheeted Riemann surface. We determine estimates of the number of resonances in complex discs at large radius. We consider resonances of an Euler-Bernoulli operator on the real line with the positive coefficients which are constants outside some finite interval. We show that the Euler-Bernoulli operator has no eigenvalues and resonances iff the positive coefficients are constants on the whole axis.

AB - We consider fourth order ordinary differential operator with compactly supported coefficients on the line. We define resonances as zeros of the Fredholm determinant which is analytic on a four sheeted Riemann surface. We determine estimates of the number of resonances in complex discs at large radius. We consider resonances of an Euler-Bernoulli operator on the real line with the positive coefficients which are constants outside some finite interval. We show that the Euler-Bernoulli operator has no eigenvalues and resonances iff the positive coefficients are constants on the whole axis.

KW - Fourth order operators

KW - resonances

KW - scattering

KW - trace formula

UR - http://www.scopus.com/inward/record.url?scp=85062000649&partnerID=8YFLogxK

U2 - 10.3233/ASY-181489

DO - 10.3233/ASY-181489

M3 - Article

VL - 111

SP - 137

EP - 177

JO - Asymptotic Analysis

JF - Asymptotic Analysis

SN - 0921-7134

IS - 3-4

ER -