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New range theorems for the dual Radon transform


Author: Alexander Katsevich
Journal: Trans. Amer. Math. Soc. 353 (2001), 1089-1102
MSC (2000): Primary 44A12
DOI: https://doi.org/10.1090/S0002-9947-00-02641-6
Published electronically: October 11, 2000
MathSciNet review: 1804413
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Abstract:

Three new range theorems are established for the dual Radon transform $R^*$: on $C^\infty$ functions that do not decay fast at infinity (and admit an asymptotic expansion), on $\mathcal{S}(Z_n)$, and on $C_0^\infty(Z_n)$. Here $Z_n:=S^{n-1}\times\mathbb{R}$, and $R^*$ acts on even functions $\mu(\alpha,p)=\mu(-\alpha,-p), (\alpha,p)\in Z_n$.


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Additional Information

Alexander Katsevich
Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
Email: akatsevi@pegasus.cc.ucf.edu

DOI: https://doi.org/10.1090/S0002-9947-00-02641-6
Keywords: Dual Radon transform, range theorems, asymptotic expansions
Received by editor(s): January 20, 1998
Received by editor(s) in revised form: June 24, 1999
Published electronically: October 11, 2000
Additional Notes: This research was supported in part by NSF grant DMS-9704285
Article copyright: © Copyright 2000 American Mathematical Society

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