On Single Measurement Stability for the Fractional Calder\'on Problem
Abstract
In this short note we prove the logarithmic stability of the single measurement uniqueness result for the fractional Calder\'on problem which had been derived in GRSU18. To this end, we use the quantitative uniqueness results established in RS20a and complement these bounds with a boundary doubling estimate. The latter yields control of the order of vanishing of solutions to the fractional Schr\"odinger equation. Then, following a scheme introduced in S10,ASV13 in the context of the determination of a surface impedance from far field measurements, this allows us to deduce logarithmic stability of the potential q.
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