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

2020/05/07 by Rubin, Boris
#44A12 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2005.03607

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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