Resonances of 4th order differential operators
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.