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An Inversion Formula of the Radon Transform on the Heisenberg Group

Published online by Cambridge University Press:  20 November 2018

Jianxun He
Jianxun He*
Affiliation:
Department of Mathematics College of Sciences Guihuagang Campus Guangzhou University Guangzhou 510405 People’s Republic of China, e-mail: [email protected]
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Abstract

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In 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.

Keywords

43A8544A15wavelet transformRadon transformHeisenberg group
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 3 , 01 September 2004 , pp. 389 - 397
Copyright
Copyright © Canadian Mathematical Society 2004

References

[1] Feichtinger, H. G. and Gröchenig, K. H., Banach Spaces Related to Integrable Group Representations and Their Atomic Decompositions. J. Funct. Anal. 86 (1989), 307–340.Google Scholar
[2] Geller, D., Fourier Analysis on the Heisenberg Group I. J. Funct. Anal. 36 (1980), 205–254.Google Scholar
[3] He, J., Continuous Multiscale Analysis on the Heisenberg Group. Bull. KoreanMath. Soc. 38 (2001), 517–526.Google Scholar
[4] He, J. and Liu, H., Admissible Wavelets Associated with the Affine Automorphism Group of the Siegel Upper Half-Plane. J. Math. Anal. Appl. 208 (1997), 58–70.Google Scholar
[5] Helgason, S., The Radon Transform. Second Edition, Birkhäuser, Boston Basel Berlin, 1999.Google Scholar
[6] Holschneider, M., Inverse Radon Transforms Through InverseWavelet Transforms. Inverse Problems 7 (1991), 853–861.Google Scholar
[7] Liu, H. and Peng, L., Admissible Wavelets Associated with the Heisenberg Group. Pacific Math. J. 180 (1997), 101–123.Google Scholar
[8] Nessibi, M. M. and Trimèche, K., Inversion of the Radon Transform on the Laguerre Hypergroup by Using Generalized Wavelets. J. Math. Anal. Appl. 208 (1997), 337–363.Google Scholar
[9] Rubin, B., The Calder´on Reproducing Formula,Windowed X-ray Transforms and Radon Transforms in Lp-spaces. J. Fourier Anal. Appl. 4 (1998), 175–197.Google Scholar
[10] Rubin, B., Fractional Calculus and Wavelet Transforms in Integral Geometry. Fract. Calculus Appl. Anal. 1 (1998), 193–219.Google Scholar
[11] Seaborn, J. B., Hypergeometric Functions and Their Applications. Springer-Verlag, New York, Berlin, Heidelberg, London, 1991.Google Scholar
[12] Strichartz, R. S., Lp Harmonic Analysis and Radon Transforms on the Heisenberg Group. J. Funct. Anal. 96 (1991), 350–406.Google Scholar
[13] Thangavelu, S., Harmonic Analysis on the Heisenberg Group. Birkhäuser, Boston, Basel, Berlin, 1998.Google Scholar