Exponential instability in the fractional Calderón problem
In this paper we prove the exponential instability of the fractional Calderón problem and thus prove the optimality of the logarithmic stability estimate from Rüland and Salo (2017 arXiv:1708.06294). In order to infer this result, we follow the strategy introduced by Mandache in (2001 Inverse Prob...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
20 February 2018
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| In: |
Inverse problems
Year: 2018, Volume: 34, Issue: 4, Pages: 1-21 |
| ISSN: | 1361-6420 |
| DOI: | 10.1088/1361-6420/aaac5a |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1088/1361-6420/aaac5a
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| Author Notes: | Angkana Rüland and Mikko Salo |
| Summary: | In this paper we prove the exponential instability of the fractional Calderón problem and thus prove the optimality of the logarithmic stability estimate from Rüland and Salo (2017 arXiv:1708.06294). In order to infer this result, we follow the strategy introduced by Mandache in (2001 Inverse Problems 17 1435) 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 Rüland and Salo (2017 arXiv:1708.06294). Finally, in one dimension, we show a close relation between the fractional Calderón problem and the truncated Hilbert transform. |
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| Item Description: | Gesehen am 19.05.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1361-6420 |
| DOI: | 10.1088/1361-6420/aaac5a |