Characterizations of function spaces by the discrete Radon transform

A. Abouelaz, T. Kawazoe

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)627-637
Number of pages11
JournalIntegral Transforms and Special Functions
Volume23
Issue number9
DOIs
Publication statusPublished - 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

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