A1 Journal article (refereed)
Uniqueness and reconstruction for the fractional Calderón problem with a single measurement (2020)

Ghosh, T., Rüland, A., Salo, M., & Uhlmann, G. (2020). Uniqueness and reconstruction for the fractional Calderón problem with a single measurement. Journal of Functional Analysis, 279, 1. https://doi.org/10.1016/j.jfa.2020.108505

JYU authors or editors

Publication details

All authors or editors: Ghosh, Tuhin; Rüland, Angkana; Salo, Mikko; Uhlmann, Gunther

Journal or series: Journal of Functional Analysis

ISSN: 0022-1236

eISSN: 1096-0783

Publication year: 2020

Volume: 279

Pages range: 1

Article number: 108505

Publisher: Academic Press

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1016/j.jfa.2020.108505

Publication open access: Not open

Publication channel open access: 

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/68537

Publication is parallel published: https://arxiv.org/abs/1801.04449

Abstract

We show global uniqueness in the fractional Calderón problem with a single measurement and with data on arbitrary, possibly disjoint subsets of the exterior. The previous work [10] considered the case of infinitely many measurements. The method is again based on the strong uniqueness properties for the fractional equation, this time combined with a unique continuation principle from sets of measure zero. We also give a constructive procedure for determining an unknown potential from a single exterior measurement, based on constructive versions of the unique continuation result that involve different regularization schemes.

Keywords: functional analysis

Free keywords: Calderón problem; functional analysis

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Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 2