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We use the classical Fourier analysis to introduce analytic families ofweighted differential operators on the unit sphere. These operators arepolynomial functions of the usual Beltrami-Laplace operator. New inversionformulas are obtained for totally geodesic Funk transforms on the sphere andthe correpsonding lambda-cosine transforms.

The Fourier Transform Approach to Inversion of lambda-Cosine and Funk Transforms on the Unit Sphere