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arXiv · 1711.04799

Exponential instability in the fractional Calderón problem

Angkana Rüland·Mikko Salo
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Abstract

In this note we prove the exponential instability of the fractional Calderón problem and thus prove the optimality of the logarithmic stability estimate from \cite{RS17}. In order to infer this result, we follow the strategy introduced by Mandache in \cite{M01} for the standard Calderón problem. Here we exploit a close relation between the fractional Calderón problem and the classical Poisson operator. Moreover, using the construction of a suitable orthonormal basis, we also prove (almost) optimality of the Runge approximation result for the fractional Laplacian, which was derived in \cite{RS17}. Finally, in one dimension, we show a close relation between the fractional Calderón problem and the truncated Hilbert transform.

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Angkana Rüland, Mikko Salo. 2017-11-13. Exponential instability in the fractional Calderón problem. https://doi.org/10.1088/1361-6420%2Faaac5a

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