Resonances for Euler–Bernoulli operator on the half-line

Результат исследований: Научные публикации в периодических изданияхстатьянаучнаярецензирование

3 Цитирования (Scopus)

Выдержка

We consider resonances for fourth order differential operators on the half-line with compactly supported coefficients. We determine asymptotics of a counting function of resonances in complex discs at large radius, describe the forbidden domain for resonances and obtain trace formulas in terms of resonances. We apply these results to the Euler–Bernoulli operator on the half-line. The coefficients of this operator are positive and constants outside a finite interval. We show that this operator does not have any eigenvalues and resonances iff its coefficients are constants on the whole half-line.

Язык оригиналаанглийский
Страницы (с-по)534-566
Число страниц33
ЖурналJournal of Differential Equations
Том263
Номер выпуска1
DOI
СостояниеОпубликовано - 5 июл 2017

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    Предметные области Scopus

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    abstract = "We consider resonances for fourth order differential operators on the half-line with compactly supported coefficients. We determine asymptotics of a counting function of resonances in complex discs at large radius, describe the forbidden domain for resonances and obtain trace formulas in terms of resonances. We apply these results to the Euler–Bernoulli operator on the half-line. The coefficients of this operator are positive and constants outside a finite interval. We show that this operator does not have any eigenvalues and resonances iff its coefficients are constants on the whole half-line.",
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    author = "Andrey Badanin and Korotyaev, {Evgeny L.}",
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    Resonances for Euler–Bernoulli operator on the half-line. / Badanin, Andrey; Korotyaev, Evgeny L.

    В: Journal of Differential Equations, Том 263, № 1, 05.07.2017, стр. 534-566.

    Результат исследований: Научные публикации в периодических изданияхстатьянаучнаярецензирование

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    N2 - We consider resonances for fourth order differential operators on the half-line with compactly supported coefficients. We determine asymptotics of a counting function of resonances in complex discs at large radius, describe the forbidden domain for resonances and obtain trace formulas in terms of resonances. We apply these results to the Euler–Bernoulli operator on the half-line. The coefficients of this operator are positive and constants outside a finite interval. We show that this operator does not have any eigenvalues and resonances iff its coefficients are constants on the whole half-line.

    AB - We consider resonances for fourth order differential operators on the half-line with compactly supported coefficients. We determine asymptotics of a counting function of resonances in complex discs at large radius, describe the forbidden domain for resonances and obtain trace formulas in terms of resonances. We apply these results to the Euler–Bernoulli operator on the half-line. The coefficients of this operator are positive and constants outside a finite interval. We show that this operator does not have any eigenvalues and resonances iff its coefficients are constants on the whole half-line.

    KW - Fourth order operators

    KW - Resonances

    KW - Scattering

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