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


Ghosh, Tuhin; Rüland, Angkana; Salo, Mikko; Uhlmann, Gunther (2020). Uniqueness and reconstruction for the fractional Calderón problem with a single measurement. Journal of Functional Analysis, 279, 1, 108505. DOI: 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: http://doi.org/10.1016/j.jfa.2020.108505

Open Access: Publication channel is not openly available

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


Contributing organizations


Related projects

Centre of Excellence in Inverse Modelling and Imaging
Salo, Mikko
Academy of Finland
01/01/2018-31/12/2020
Inverse boundary problems: toward a unified theory
Salo, Mikko
Academy of Finland
01/09/2017-31/08/2021
Inverse boundary problems - toward a unified theory
Salo, Mikko
European Commission
01/05/2018-30/04/2023


Ministry reporting: Yes

Reporting Year: 2020

Preliminary JUFO rating: 2


Last updated on 2020-09-07 at 23:08