Radon transform on a space over a residue class ring

V. F. Molchanov

Tambov State University

Abstract: 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: Radon transform, residue class ring, Möbius function, function algebras.

UDC: 517.444

MSC: Primary 44A12; Secondary 13M99, 15A18

Received: 29.12.2010 and 29.12.2011

DOI: 10.4213/sm7838

 English version: Sbornik: Mathematics, 2012, 203:5, 727–742

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