Spherical Radon Transform and Related Wavelet Transforms

Continuous wavelet transforms associated with the spherical Radon transform Rf on the n-dimensional unit sphere double-struck S signⁿ, n ≥ 2, are introduced. It is assumed that f ∈ L^p(double-struck S signⁿ) or f ∈ C(double-struck S signⁿ). For the operator R and for its inverse R^-1 explicit representations are given in the wavelet form. As a consequence we obtain the characterization of the range of R.