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)

Access to Document

10.1155/2015/375017

Fingerprint Dive into the research topics of 'On the Range of the Radon Transform on Z n and the Related Volberg's Uncertainty Principle'. Together they form a unique fingerprint.

Cite this

@article{898ecde4f1f440cab62b260f43ad1615,

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",

year = "2015",

doi = "10.1155/2015/375017",

language = "English",

volume = "2015",

journal = "Journal of Mathematics",

issn = "2314-4629",

publisher = "Hindawi Publishing Corporation",

}

TY - JOUR

T1 - On the Range of the Radon Transform on Z n and the Related Volberg's Uncertainty Principle

AU - Abouelaz, Ahmed

AU - Ihsane, Abdallah

AU - Kawazoe, Takeshi

PY - 2015

Y1 - 2015

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=85014294216&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014294216&partnerID=8YFLogxK

U2 - 10.1155/2015/375017

DO - 10.1155/2015/375017

M3 - Article

AN - SCOPUS:85014294216

VL - 2015

JO - Journal of Mathematics

JF - Journal of Mathematics

SN - 2314-4629

M1 - 375017

ER -