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

AN - SCOPUS:85062000649

VL - 111

SP - 137

EP - 177

JO - Asymptotic Analysis

JF - Asymptotic Analysis

SN - 0921-7134

IS - 3-4

ER -