|
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.
Received: 29.12.2010 and 29.12.2011
Citation:
V. F. Molchanov, “Radon transform on a space over a residue class ring”, Mat. Sb., 203:5 (2012), 119–134; Sb. Math., 203:5 (2012), 727–742
Linking options:
https://www.mathnet.ru/eng/sm7838https://doi.org/10.1070/SM2012v203n05ABEH004240 https://www.mathnet.ru/eng/sm/v203/i5/p119
|
Statistics & downloads: |
Abstract page: | 524 | Russian version PDF: | 169 | English version PDF: | 14 | References: | 63 | First page: | 31 |
|