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

Ahmed Abouelaz; Abdallah Ihsane; Takeshi Kawazoe

doi:10.1155/2015/375017

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

Ahmed Abouelaz, Abdallah Ihsane, Takeshi Kawazoe

Faculty of Policy Management

Research output: Contribution to journal › Article › peer-review

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 language	English
Article number	375017
Journal	Journal of Mathematics
Volume	2015
DOIs	https://doi.org/10.1155/2015/375017
Publication status	Published - 2015

ASJC Scopus subject areas

Mathematics(all)

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

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.",

author = "Ahmed Abouelaz and Abdallah Ihsane and Takeshi Kawazoe",

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AB - 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.

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

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