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

Boris Rubin

备注：: 14 pages

英文摘要：

We use the classical Fourier analysis to introduce analytic families of weighted differential operators on the unit sphere. These operators are polynomial functions of the usual Beltrami-Laplace operator. New inversion formulas are obtained for totally geodesic Funk transforms on the sphere and the correpsonding lambda-cosine transforms.

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