A range theorem for the Radon transform
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- by W. R. Madych and D. C. Solmon PDF
- Proc. Amer. Math. Soc. 104 (1988), 79-85 Request permission
Abstract:
Conditions are prescribed for a function $g$ which are sufficient to ensure that it is the Radon transform of a continuous function $f$ on ${{\mathbf {R}}^n}$ such that $f(x) = O({\left | x \right |^{ - n - k - 1}})$ as $\left | x \right | \to \infty$. Roughly speaking, these criteria involve smoothness and the classical polynomial consistency conditions up to order $k$ on $g$. In particular, the result implies Helgason’s Schwartz theorem for the Radon transform [Acta Math. 113 (1965)].References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 79-85
- MSC: Primary 44A15; Secondary 26B40
- DOI: https://doi.org/10.1090/S0002-9939-1988-0958047-7
- MathSciNet review: 958047