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The Calderón reproducing formula, windowed X-ray transforms, and radon transforms in LP-spaces

  • Boris Rubin
Article

Abstract

The generalized Calderón reproducing formula involving “wavelet measure” is established for functions f ∈ Lp(ℝn). The special choice of the wavelet measure in the reproducing formula gives rise to the continuous decomposition of f into wavelets, and enables one to obtain inversion formulae for generalized windowed X-ray transforms, the Radon transform, and k-plane transforms. The admissibility conditions for the wavelet measure μ are presented in terms of μ itself and in terms of the Fourier transform of μ.

Math Subject Classifications

Primary 44A05 secondary 42B99 

Keywords and Phrases

Wavelets Radon transforms Lp-spaces windowed X-ray transforms k-plane transforms 

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Copyright information

© Birkhäuser Boston 1998

Authors and Affiliations

  • Boris Rubin
    • 1
  1. 1.Department of MathematicsThe Hebrew University of JerusalemIsrael

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