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Resonances of 4-th Order Differential Operators
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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…
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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…
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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…
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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…
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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…
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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…
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References
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Resonances of 4th order differential operators
- MathematicsAsymptot. Anal.
- 2019
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
- Mathematics
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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
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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
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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
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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
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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
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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…