Partial Data Problems and Unique Continuation in Scalar and Vector Field Tomography
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.
Main Authors
Format
Articles
Research article
Published
2022
Series
Subjects
Publication in research information system
Publisher
Birkhäuser
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202204042151Use this for linking
Review status
Peer reviewed
ISSN
1069-5869
DOI
https://doi.org/10.1007/s00041-022-09907-9
Language
English
Published in
Journal of Fourier Analysis and Applications
Citation
- 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
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Funder(s)
Research Council of Finland
Research Council of Finland
Funding program(s)
Centre of Excellence, AoF
Academy Project, AoF
Huippuyksikkörahoitus, SA
Akatemiahanke, SA
Additional information about funding
J.I. was supported by Academy of Finland (grants 332890 and 336254). K.M. was supported by Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging, grant numbers 284715 and 309963). Open Access funding provided by University of Jyväskylä (JYU).
Copyright© 2022 the Authors