A1 Journal article (refereed)
Partial Data Problems and Unique Continuation in Scalar and Vector Field Tomography (2022)


Ilmavirta, J., & Mönkkönen, K. (2022). Partial Data Problems and Unique Continuation in Scalar and Vector Field Tomography. Journal of Fourier Analysis and Applications, 28(2), Article 34. https://doi.org/10.1007/s00041-022-09907-9


JYU authors or editors


Publication details

All authors or editorsIlmavirta, Joonas; Mönkkönen, Keijo

Journal or seriesJournal of Fourier Analysis and Applications

ISSN1069-5869

eISSN1531-5851

Publication year2022

Publication date26/03/2022

Volume28

Issue number2

Article number34

PublisherBirkhäuser

Publication countrySwitzerland

Publication languageEnglish

DOIhttps://doi.org/10.1007/s00041-022-09907-9

Publication open accessOpenly available

Publication channel open accessPartially open access channel

Publication is parallel published (JYX)https://jyx.jyu.fi/handle/123456789/80472

Publication is parallel publishedhttps://arxiv.org/abs/2103.14385


Abstract

We prove that if P(D) is some constant coefficient partial differential operator and f is a scalar field such that P(D)f vanishes in a given open set, then the integrals of f over all lines intersecting that open set determine the scalar field uniquely everywhere. This is done by proving a unique continuation property of fractional Laplacians which implies uniqueness for the partial data problem. We also apply our results to partial data problems of vector fields.


Keywordsinverse problemspartial differential equationstomography

Free keywordsinverse problems; X-ray tomography; vector field tomography; region of interest tomography; unique continuation


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Ministry reportingYes

Reporting Year2022

JUFO rating2


Last updated on 2024-15-06 at 01:46