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arXiv · 1612.01683

Propagation property and its application to inverse scattering for fractional powers of the negative Laplacian

Atsuhide Ishida
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Abstract

Enss (1983) proved a propagation estimate for the usual free Schroedinger operator that turned out later to be very useful for inverse scattering in the work of Enss--Weder (1995). Since then, this method has been called the Enss--Weder time-dependent method. We study the same type of propagation estimate for the fractional powers of the negative Laplacian and, as with the Enss--Weder method, we apply our estimate to inverse scattering. We find that the high-velocity limit of the scattering operator uniquely determines the short-range interactions.

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Atsuhide Ishida. 2016-12-06. Propagation property and its application to inverse scattering for fractional powers of the negative Laplacian. https://arxiv.org/abs/1612.01683

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