## New range theorems for the dual Radon transform

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- by Alexander Katsevich PDF
- Trans. Amer. Math. Soc.
**353**(2001), 1089-1102 Request permission

## 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 $\mu (\alpha ,p)=\mu (-\alpha ,-p), (\alpha ,p)\in Z_n$.## References

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## Additional Information

**Alexander Katsevich**- Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
- MR Author ID: 320907
- Email: akatsevi@pegasus.cc.ucf.edu
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**353**(2001), 1089-1102 - MSC (2000): Primary 44A12
- DOI: https://doi.org/10.1090/S0002-9947-00-02641-6
- MathSciNet review: 1804413