scholarly journals An inversion formula of radon transform on the product Heisenberg group

2012 ◽  
Vol 42 (2) ◽  
pp. 597-615
Author(s):  
Jianxun He ◽  
Liqun Wen
Keyword(s):  
Heisenberg Group ◽  
Radon Transform ◽  
Inversion Formula

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.

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.

The d-plane radon transform on the torus $$ \mathbb{T}^n $$

2011 ◽  
Vol 14 (2) ◽  
Author(s):  
Ahmed Abouelaz
Keyword(s):  
Radon Transform ◽  
Inversion Formula ◽  
Flat Torus ◽  
Smooth Functions ◽  
Suitable Function

AbstractWe define and study the d-plane Radon transform, namely R, on the n-dimensional (flat) torus. The transformation R is obtained by integrating a suitable function f over all d-dimensional geodesics (d-planes in the torus). We specially establish an explicit inversion formula of R and we give a characterization of the image, under the d-plane Radon transform, of the space of smooth functions on the torus.

scholarly journals AN INVERSION FORMULA FOR THE GAUSSIAN RADON TRANSFORM FOR BANACH SPACES

2013 ◽  
Vol 16 (04) ◽  
pp. 1350034 ◽  
Author(s):  
IRINA HOLMES
Keyword(s):  
Banach Spaces ◽  
Radon Transform ◽  
Inversion Formula ◽  
Bargmann Transform ◽  
Abstract Wiener Spaces ◽  
Wiener Spaces

We prove a disintegration theorem for the Gaussian Radon transform Gf on Banach spaces and use the Segal–Bargmann transform on abstract Wiener spaces to find a procedure to obtain f from its Gaussian Radon transform Gf.

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