### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Analysis

### Cite this

**Characterizations of function spaces by the discrete Radon transform.** / Abouelaz, A.; Kawazoe, Takeshi.

Research output: Contribution to journal › Article

*Integral Transforms and Special Functions*, vol. 23, no. 9, pp. 627-637. https://doi.org/10.1080/10652469.2011.618928

}

TY - JOUR

T1 - Characterizations of function spaces by the discrete Radon transform

AU - Abouelaz, A.

AU - Kawazoe, Takeshi

PY - 2012/9

Y1 - 2012/9

N2 - 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).

AB - 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).

KW - characterization of the discrete Radon transform images

KW - discrete Fourier transform

KW - discrete Radon transform

KW - linear diophantine equations

UR - http://www.scopus.com/inward/record.url?scp=84865276190&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865276190&partnerID=8YFLogxK

U2 - 10.1080/10652469.2011.618928

DO - 10.1080/10652469.2011.618928

M3 - Article

AN - SCOPUS:84865276190

VL - 23

SP - 627

EP - 637

JO - Integral Transforms and Special Functions

JF - Integral Transforms and Special Functions

SN - 1065-2469

IS - 9

ER -