Geodesic
Radon transform on a~space over a~residue class ring
Sbornik. Mathematics, Tome 203 (2012) no. 5, pp. 727-742

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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, Möbius function, function algebras.
Mots-clés : Radon transform 
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     author = {V. F. Molchanov},
     title = {Radon transform on a~space over a~residue class ring},
     journal = {Sbornik. Mathematics},
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     url = {http://geodesic.mathdoc.fr/item/SM_2012_203_5_a3/}
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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/