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.

Original languageEnglish
Pages (from-to)137-177
Number of pages41
JournalAsymptotic Analysis
Issue number3-4
Publication statusPublished - 1 Jan 2019

Scopus subject areas

  • Mathematics(all)

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