The Calderón reproducing formula, windowed X-ray transforms, and radon transforms in LP-spaces
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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 ClassificationsPrimary 44A05 secondary 42B99
Keywords and PhrasesWavelets Radon transforms Lp-spaces windowed X-ray transforms k-plane transforms
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