scholarly journals The Radon transform on the Heisenberg group and the transversal Radon transform

2012 ◽  
Vol 262 (1) ◽  
pp. 234-272 ◽  
Author(s):  
B. Rubin
Keyword(s):  
Heisenberg Group ◽  
Radon Transform

An Inversion Formula of the Radon Transform on the Heisenberg Group

2004 ◽  
Vol 47 (3) ◽  
pp. 389-397 ◽  
Author(s):  
Jianxun He
Keyword(s):  
Heisenberg Group ◽  
Radon Transform ◽  
Inversion Formula ◽  
Weak Sense

AbstractIn this paper we give an inversion formula of the Radon transform on the Heisenberg group by using the wavelets defined in [3]. In addition, we characterize a space such that the inversion formula of the Radon transform holds in the weak sense.

Radial wavelet and radon transform on the Heisenberg group

2012 ◽  
Vol 93 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Mingkai Yin ◽  
Jianxun He
Keyword(s):  
Heisenberg Group ◽  
Radon Transform

scholarly journals The Radon Transforms on the Generalized Heisenberg Group

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Tianwu Liu ◽  
Jianxun He
Keyword(s):  
Fourier Transform ◽  
Differential Operator ◽  
Heisenberg Group ◽  
Radon Transform ◽  
Inversion Formula ◽  
The Other ◽  
Radon Transforms

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.

scholarly journals Littlewood-Paley g-function and Radon Transform on the Heisenberg Group

2018 ◽  
Vol 11 (1) ◽  
pp. 138
Author(s):  
Zheng Fang ◽  
Jianxun He
Keyword(s):  
Heisenberg Group ◽  
Radon Transform ◽  
Unitary Operator ◽  
Radon Transforms ◽  
Inversion Formulas ◽  
Poisson Integrals

In this paper, we consider Radon transform on the Heisenberg group $\textbf{H}^{n}$, and obtain new inversion formulas via dual Radon transforms and Poisson integrals. We prove that the Radon transform is a unitary operator from Sobelov space $W$ into $L^{2}(\textbf{H}^{n})$. Moreover, we use the Radon transform to define the Littlewood-Paley $g$-function on a hyperplane and obtain the Littlewood-Paley theory.

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