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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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