Exponential instability in the fractional Calderón problem
In this note we prove the exponential instability of the fractional Calder\'on 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 Calder\'o...
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| Main Authors: | , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
13 Nov 2017
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| In: |
Arxiv
Year: 2017, Pages: 1-17 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1711.04799
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| Author Notes: | Angkana Rüland and Mikko Salo |
| Summary: | In this note we prove the exponential instability of the fractional Calder\'on 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 Calder\'on problem. Here we exploit a close relation between the fractional Calder\'on 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 Calder\'on problem and the truncated Hilbert transform. |
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| Item Description: | Gesehen am 19.05.2021 |
| Physical Description: | Online Resource |