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Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 1
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Articles

Radial wavelet and radon transform on the Heisenberg group

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Pages 1-13 | Received 19 May 2012, Accepted 11 Nov 2012, Published online: 17 Dec 2012

References

  • He JX, Liu HP. Admissible wavelets associated with the affine automorphism group of the Siegel upper half-plane. J. Math. Anal. Appl. 1997;208:58–70.
  • Liu HP, Peng LZ. Admissible wavelets associated with the Heisenberg group. Pac. J. Math. 1997;180:101–123.
  • Geller D, Mayeli A. Continuous wavelet and frames on stratified Lie groups I. J. Four. Anal. Appl. 2006;12:543–579.
  • He JX, Liu HP. Admissible wavelets and inverse radon transform associated with the affine homogeneous Siegel domains of type II. Commun. Anal. Geom. 2007;15:1–28.
  • He JX, Liu HP. Inversion of the radon transform associated with the classical domain of type one. Intern. J. Math. 2005;16:875–887.
  • Ishi H. Wavelet transform for semidirect product groups with not necessarily commutative normal subgroup. J. Four. Anal. Appl. 2006;12:37–52.
  • Helgason S. Integral Geometry and Radon Transforms. New York, NY: Springer; 2010.
  • He JX. An inversion formula of the radon transform on the Heisenberg group. Canad. Math. Bull. 2004;47:389–397.
  • Holschneider M. Inverse radon transforms through inverse wavelet transfroms. Inv. Probl. 1991;7:853–861.
  • Rubin B. Calderón reproducing formula, windowed X-ray transforms, and radon transforms in Lp-spaces. J. Four. Anal. Appl. 1998;4:175–197.
  • Rubin B. Convolution-backprojection method for the k-plane transform, and Calderón’s identity for ridgelet transforms. Appl. Comput. Harmon. Anal. 2004;16:231–242.
  • Rubin B. The Radon transform on the Heisenberg group and the transversal radon transform. J. Funct. Anal. 2012;262:234–272.
  • Strichartz RS. Lp harmonic analysis and radon transforms on the Heisenberg group. J. Funct. Anal. 1991;96:350–406.
  • Folland GB. Harmonic Analysis in the Phase Space. Princeton, NJ: Princeton University Press; 1989.
  • Geller D. Fourier analysis on the Heisenberg group. J. Funct. Anal. 1980;26:205–254.
  • Thangavelu S. Harmonic analysis on the Heisenberg group. Boston, MA: Birkhäuser; 1998.
  • Stein EM. Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals. Princeton, NJ: Princeton University Press; 1993.

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