Abstract
We derive a dispersion estimate for one-dimensional perturbed radial Schr\"odinger operators. We also derive several new estimates for solutions of the underlying differential equation and investigate the behavior of the Jost function near the edge of the continuous spectrum.
Highlights
We are concerned with the one-dimensional Schrodinger equation iψ(t, x) = Hψ(t, x), H
Our present paper should be understood as a contribution to understanding the properties of solutions of the underlying spectral problem. In this respect we would like to emphasize that the behavior of the Jost function near the bottom of the essential spectrum is still not understood satisfactorily, and for this very reason the resonant case had to be excluded from our main theorem
(n−2)2 4 could be included in this discussion as it can be absorbed in the definition of s [3,4]
Summary
Our present paper should be understood as a contribution to understanding the properties of solutions of the underlying spectral problem In this respect we would like to emphasize that the behavior of the Jost function near the bottom of the essential spectrum is still not understood satisfactorily, and for this very reason the resonant case had to be excluded from our main theorem. This is definitely a gap which should be filled. (n−2) could be included in this discussion as it can be absorbed in the definition of s [3,4]
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