Geodesic
Radon transform on a space over a residue class ring
Sbornik. Mathematics, Tome 203 (2012) no. 5, pp. 727-742 Cet article a éte moissonné depuis la source Math-Net.Ru

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The functions on a space of dimension $N$ over the residue class ring $\mathbb Z_n$ modulo $n$ that are invariant with respect to the group $\operatorname{GL}(N,\mathbb Z_n)$ form a commutative convolution algebra. We describe the structure of this algebra and find the eigenvectors and eigenvalues of the operators of multiplication by elements of this algebra. The results thus obtained are applied to solve the inverse problem for the hyperplane Radon transform on $\mathbb Z^N_n$. Bibliography: 2 titles.
Keywords: residue class ring, function algebras.
Mots-clés : Radon transform, Möbius function 
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     title = {Radon transform on a~space over a~residue class ring},
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V. F. Molchanov. Radon transform on a space over a residue class ring. Sbornik. Mathematics, Tome 203 (2012) no. 5, pp. 727-742. http://geodesic.mathdoc.fr/item/SM_2012_203_5_a3/

[1] M. I. Graev, N. V. Pavlenko, “The Radon transformation in the space ${\rm P}^n(A)$ where $A$ is a finite commutative ring with identity”, Soviet Math. Dokl., 13:4 (1972), 1493–1497 | MR | Zbl

[2] M. Hall, Combinatorial theory, Blaisdell Publ., Waltham, MA–Toronto–London, 1967 | MR | MR | Zbl | Zbl