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On the range of the attenuated Radon transform in strictly convex sets


Authors: Kamran Sadiq and Alexandru Tamasan
Journal: Trans. Amer. Math. Soc. 367 (2015), 5375-5398
MSC (2010): Primary 30E20; Secondary 35J56
DOI: https://doi.org/10.1090/S0002-9947-2014-06307-1
Published electronically: November 4, 2014
MathSciNet review: 3347176
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Abstract: We present new necessary and sufficient conditions for a function on $ \partial \Omega \times S^1$ to be in the range of the attenuated Radon transform of a sufficiently smooth function support in the convex set $ \overline \Omega \subset \mathbb{R}^2$. The approach is based on an explicit Hilbert transform associated with traces on the boundary of A-analytic functions in the sense of Bukhgeim.


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Additional Information

Kamran Sadiq
Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
Address at time of publication: Johann Radon Institute for Computational and Applied Mathematics (RICAM), Altenbergerstrasse 69, A-4040 Linz, Austria
Email: ksadiq@knights.ucf.edu, kamran.sadiq@ricam.oeaw.ac.at

Alexandru Tamasan
Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
Email: tamasan@math.ucf.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06307-1
Keywords: Attenuated Radon transform, A-analytic maps, Hilbert transform
Received by editor(s): May 24, 2013
Published electronically: November 4, 2014
Article copyright: © Copyright 2014 American Mathematical Society

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