Spherical Radon Transform and Related Wavelet Transforms

Abstract Continuous wavelet transforms associated with the spherical Radon transformRfon then-dimensional unit sphere S n,n≥ 2, are introduced. It is assumed thatf ∈ Lp( S n) orf ∈ C( S n). For the operatorRand for its inverseR−1explicit representations are given in the wavelet form. As a consequence we obtain the characterization of the range ofR.

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