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The Fourier Transform Approach to Inversion of lambda-Cosine and Funk Transforms on the Unit Sphere
Published 7 May 2020 in math.FA | (2005.03607v2)
Abstract: 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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