### Abstract

Let ℤ ^{n} be the lattice in ℝ ^{n} and G the set of all discrete hyperplanes in ℤ ^{n}. Similarly, as in the Euclidean case, for a function f on ℤ ^{n}, the discrete Radon transform Rf is defined by the integral of f over discrete hyperplanes, and R maps functions on ℤ ^{n} to functions on G. In this paper, we determine the Radon transform images of the Schwartz space S(ℤ ^{n}), the space of compactly supported functions on ℤ ^{}, and a discrete Hardy space H ^{1}(ℤ ^{n}).

Original language | English |
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Pages (from-to) | 627-637 |

Number of pages | 11 |

Journal | Integral Transforms and Special Functions |

Volume | 23 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2012 Sep 1 |

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### Keywords

- characterization of the discrete Radon transform images
- discrete Fourier transform
- discrete Radon transform
- linear diophantine equations

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics