Spherical Radon transform and related wavelet transforms (Q1267270)

The author introduces the continuous wavelet transform associated with the spherical Radon transform \(Rf\) on the \(n\)-dimensional unit sphere \({\mathbf S}^n\), \(n\geq 2\), where \(f\in L^p({\mathbf S}^n)\) or \(f\in C({\mathbf S}^n)\). Explicit wavelet representations for the spherical Radon transform \(R\) and for its inverse transform \(R^{-1}\) are given. The range of the spherical Radon transform \(R\) is described as well.