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Spectral asymptotics for the third order operator with periodic coefficients
Andrey Badanin, Evgeny Korotyaev
We consider the self-adjoint third order operator with 1-periodic coefficients on the real line. The spectrum of the operator is absolutely continuous and covers the real line. We…
Third order operator with periodic coefficients on the real line
A. Badanin, E. Korotyaev
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…
Sharp asymptotics of the quasimomentum
Evgeny L. Korotyaev
We consider the Schrödinger operator with a periodic potential on the real line. We assume that belongs to the Sobolev space $\mH_m$ on the circle for some , and w…
On the resonances and eigenvalues for a 1D half-crystal with localised impurity
Evgeny L. Korotyaev, Karl Michael Schmidt
We consider the Schrödinger operator on the half-line with a periodic potential plus a compactly supported potential . For generic , its essential spectrum has an inf…
Resonance theory for perturbed Hill operator
Evgeny Korotyaev
We consider the Schrödinger operator with a periodic potential plus a compactly supported potential on the real line. The spectrum of consists of an abs…
Trace formulas for Schrödinger operators from the view point of complex analysis
Hiroshi Isozaki, Evgeny L. Korotyaev
We consider the Schr{ö}dinger operator in with a real short-range (integrable) potential . Using the associated Fredholm determinant, we present new t…