A1 Journal article (refereed)
Exponential instability in the fractional Calderón problem (2018)

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

JYU authors or editors

Publication details

All authors or editors: Rüland, Angkana; Salo, Mikko

Journal or series: Inverse Problems

ISSN: 0266-5611

eISSN: 1361-6420

Publication year: 2018

Volume: 34

Issue number: 4

Article number: 045003

Publisher: Institute of Physics

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1088/1361-6420/aaac5a

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/57168


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.

Keywords: inverse problems

Free keywords: Calderón problem; Poisson operator; Hilbert transform

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Ministry reporting: Yes

Reporting Year: 2018

JUFO rating: 2

Last updated on 2021-17-09 at 15:58