The Radon Transforms on the Generalized Heisenberg Group-Reference-Cited by-同舟云学术

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The Radon Transforms on the Generalized Heisenberg Group

Published:2014-01-02 Issue: Volume:2014 Page:1-7
ISSN:2090-4665
Container-title:ISRN Mathematical Analysis
language:en
Short-container-title:ISRN Mathematical Analysis

Author:

Liu Tianwu¹²^ORCID,He Jianxun¹²^ORCID

Affiliation:

1. School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China

2. Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006, China

Abstract

Let Hna be the generalized Heisenberg group. In this paper, we study the inversion of the Radon transforms on Hna. Several kinds of inversion Radon transform formulas are established. One is obtained from the Euclidean Fourier transform; the other is derived from the differential operator with respect to the center variable t. Also by using sub-Laplacian and generalized sub-Laplacian we deduce an inversion formula of the Radon transform on Hna.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

General Medicine

Link

http://downloads.hindawi.com/archive/2014/490601.pdf

Reference17 articles.

1. Integral Geometry and Radon Transforms

2. Inverse Radon transforms through inverse wavelet transforms

3. The Calderón reproducing formula, windowed X-ray transforms, and radon transforms in LP-spaces

4. Lp harmonic analysis and Radon transforms on the Heisenberg group

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