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- W2168435837 abstract "Let g be a compactly supported function of d -planes in R n . We prove that then g is in the range of the Radon transform if and only if g satisfies an ultrahyperbolic system of PDEs. We parameterize the d -planes by d + 1 points x 0 , x 1 , …, x d on them and get the PDE ∂ 2 ∂x i k ∂x j 1 − ∂ 2 ∂x i 1 ∂x j k g(x 0 , x 1 , …, x d ) Vol {x i − x 0 } i = 1,d = 0 where x i k denotes the k th coordinate of x 1 . At the end we analyze in detail the case of d = 1." @default.
- W2168435837 created "2016-06-24" @default.
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- W2168435837 date "1991-10-01" @default.
- W2168435837 modified "2023-10-16" @default.
- W2168435837 title "A characterization of the Radon transform's range by a system of PDEs" @default.
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- W2168435837 doi "https://doi.org/10.1016/0022-247x(91)90371-6" @default.
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