The Calderon reproducing formula, windowed X-ray transforms, and radon transforms in Lp-Spaces

The generalized Calderon reproducing formula involving "wavelet measure" is established for functions f is an element of L-p(R-n). 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 mu are presented in terms of mu itself and in terms of the Fourier transform of mu.