On the Range of the Radon Transform on Z n and the Related Volberg's Uncertainty Principle

Ahmed Abouelaz, Abdallah Ihsane, Takeshi Kawazoe

Research output: Contribution to journal › Article

Abstract

We characterize the image of exponential type functions under the discrete Radon transform R on the lattice Z n of the Euclidean space R n n ≥ 2. We also establish the generalization of Volberg's uncertainty principle on Z n, which is proved by means of this characterization. The techniques of which we make use essentially in this paper are those of the Diophantine integral geometry as well as the Fourier analysis.

Original languageEnglish
Article number375017
JournalJournal of Mathematics
Volume2015
DOIs
Publication statusPublished - 2015

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Integral Geometry
Uncertainty Principle
Exponential Type
Radon Transform
Fourier Analysis
Euclidean space
Range of data
Generalization

ASJC Scopus subject areas

  • Mathematics(all)

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On the Range of the Radon Transform on Z n and the Related Volberg's Uncertainty Principle. / Abouelaz, Ahmed; Ihsane, Abdallah; Kawazoe, Takeshi.

In: Journal of Mathematics, Vol. 2015, 375017, 2015.

Research output: Contribution to journal › Article

Abouelaz, A, Ihsane, A & Kawazoe, T 2015, 'On the Range of the Radon Transform on Z n and the Related Volberg's Uncertainty Principle', Journal of Mathematics, vol. 2015, 375017. https://doi.org/10.1155/2015/375017
Abouelaz A, Ihsane A, Kawazoe T. On the Range of the Radon Transform on Z n and the Related Volberg's Uncertainty Principle. Journal of Mathematics. 2015;2015. 375017. https://doi.org/10.1155/2015/375017
Abouelaz, Ahmed ; Ihsane, Abdallah ; Kawazoe, Takeshi. / On the Range of the Radon Transform on Z n and the Related Volberg's Uncertainty Principle. In: Journal of Mathematics. 2015 ; Vol. 2015.
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