Totally Geodesic Radon Transform of Lp-Functions on Real Hyperbolic Space

  • Carlos A. Berenstein
  • Boris Rubin
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


We present a brief discussion of the interrelations between integral geometry and harmonic analysis and then proceed to the d-dimensional totally geodesic Radon transform f, assuming f ¡Ê L p (Hn), where Hn is the n-dimensional real hyperbolic space, and 1 ¡Ü d ¡Ü n - 1. We show that f is well defined if and only if 1 ¡Ü p < (n -1)/(d - 1) and prove estimates of the Solmon type. By making use of the convolution-backprojection method, approximation to the identity, and the corresponding wavelet-like transforms, we obtain new approximate and explicit inversion formulas for f.


Invariant Measure Convex Body Fractional Calculus Inversion Formula Fractional Integral 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Carlos A. Berenstein
    • 1
  • Boris Rubin
    • 2
  1. 1.Institute for Systems ResearchUniversity of MarylandUSA
  2. 2.Institute of MathematicsHebrew UniversityJerusalemIsrael

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