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

Salo, Mikko

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

Abstract

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

Fields of science: