Exponential instability in the fractional Calderón problem
Rüland, A., & Salo, M. (2018). Exponential instability in the fractional Calderón problem. Inverse Problems, 34(4), Article 045003. https://doi.org/10.1088/1361-6420/aaac5a
Published inInverse Problems
© the Authors, 2018. This is an open access article distributed under the terms of the Creative Commons License.
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.
PublisherInstitute of Physics
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Related funder(s)Academy of Finland; European Commission
Funding program(s)Centre of Excellence, AoF; Academy Project, AoF; FP7 (EU's 7th Framework Programme)
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about fundingMS is supported by the Academy of Finland (Finnish Centre of Excellence in Inverse Problems Research, grant numbers 284715 and 309963) and an ERC Starting Grant (grant number 307023).
Except where otherwise noted, this item's license is described as © the Authors, 2018. This is an open access article distributed under the terms of the Creative Commons License.
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