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

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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.

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Authors and Affiliations

  1. Department of Mathematics, The Hebrew University of Jerusalem, Israel

    Boris Rubin

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  1. Boris Rubin
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Communicated by Carlos A. Berenstein

Acknowledgements and Notes. Partially sponsored by the Edmund Landau Center for research in Mathematical Analysis, supported by the Minerva Foundation (Germany).

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Rubin, B. The Calderón reproducing formula, windowed X-ray transforms, and radon transforms in LP-spaces. The Journal of Fourier Analysis and Applications 4, 175–197 (1998). https://doi.org/10.1007/BF02475988

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  • DOI: https://doi.org/10.1007/BF02475988

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