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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)

Abstract

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.

Keywords

Invariant Measure Convex Body Fractional Calculus Inversion Formula Fractional Integral 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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