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Recovering asymptotics of potentials from the scattering of relativistic Schr\"odinger operators

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arxiv 2508.12463 v1 pith:DHUR33OX submitted 2025-08-17 math.AP

Recovering asymptotics of potentials from the scattering of relativistic Schr\"odinger operators

classification math.AP
keywords scatteringasymptoticspotentialsdecayingdeltaenergyfixedfrac
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We study the stationary scattering for $(-\Delta)^{\frac 12} + V(x)$ on $\mathbb{R}^3$. For poly-homogeneous potentials decaying at infinity, we prove that the asymptotics of the potential can be recovered from the scattering matrix at a fixed energy.

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