Resonances of third order differential operators

@article{Korotyaev2019ResonancesOT,
  title={Resonances of third order differential operators},
  author={Evgeny L. Korotyaev},
  journal={Journal of Mathematical Analysis and Applications},
  year={2019}
}
  • E. Korotyaev
  • Published 6 May 2016
  • Mathematics
  • Journal of Mathematical Analysis and Applications

Figures from this paper

Resonances of 4-th Order Differential Operators
We consider fourth order ordinary differential operator with compactly supported coefficients on the line. We determine asymptotics of the number of resonances in complex discs at large radius. We
Resonances of 4th order differential operators
TLDR
It is shown that the Euler-Bernoulli operator has no eigenvalues and resonances iff the positive coefficients are constants on the whole axis iff they are constants outside some finite interval.
Resonances of 4-th order differential operators on the line
We consider resonances of fourth order ordinary differential operator with compactly supported coefficients on the line. We determine estimates of the number of resonances in complex discs at large
Asymptotics of determinants of 4‐th order operators at zero
We consider fourth order ordinary differential operators on the half‐line and on the line, where the perturbation has compactly supported coefficients. The Fredholm determinant for this operator is
Third-order operators with three-point conditions associated with Boussinesq's equation
We consider a non-self-adjoint third-order operator on the interval with real 1-periodic coefficients and three-point Dirichlet conditions at the points 0, 1 and 2. The eigenvalues of this operator
Inverse resonance scattering for massless Dirac operators on the real line
We consider massless Dirac operators on the real line with compactly supported potentials. We solve two inverse problems: in terms of zeros of reflection coefficient and in terms of poles of
Inverse problems for Jacobi operators with finitely supported perturbations
We solve the inverse problem for Jacobi operators on the half lattice with finitely supported perturbations, in particular, in terms of resonances. Our proof is based on the results for the inverse
Inverse resonance scattering on rotationally symmetric manifolds
We discuss inverse resonance scattering for the Laplacian on a rotationally symmetric manifold M = ( 0 , ∞ ) × Y whose rotation radius is constant outside some compact interval. The Laplacian on M is

References

SHOWING 1-10 OF 61 REFERENCES
Resonances of 4th order differential operators
TLDR
It is shown that the Euler-Bernoulli operator has no eigenvalues and resonances iff the positive coefficients are constants on the whole axis iff they are constants outside some finite interval.
Determination of a third-order operator from two of its spectra
We consider a complex third-order differential operator on a bounded interval with boundary conditions presenting a mixed aspect of the Dirichlet and the periodic problems. It is proved that two
Resonances for 1d Stark operators
We consider the Stark operator perturbed by a compactly supported potential (of a certain class) on the real line. We prove the following results: (a) upper and lower bounds on the number of
Third order operator with periodic coefficients on the real line
We consider the third order operator with periodic coefficients on the real line. This operator is used in the integration of the non-linear evolution Boussinesq equation. For the minimal smoothness
On the Inverse Resonance Problem
A new technique is presented which gives conditions under which perturbations of certain base potentials are uniquely determined from the location of eigenvalues and resonances in the context of a
Asymptotic Distribution of Resonances in One Dimension
Abstract We determine the leading asymptotics of the resonance counting function for a class of Schrodinger operators in one dimension whose potentials may have non-compact support.
Stability for inverse resonance problem
For the Schrodinger operator on the half line, we show that if ϰ0={ϰ0}1∞ is a sequence of zeroes (eigenvalues and resonances) of the Jost function for some real compactly supported potential q 0 and
...
...