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.
Lacunary polynomials in $L^1$: geometry of the unit sphere
The trace as an average over the unit sphere of a normed space with a 1-symmetric basis
On Uniform Homeomorphisms of the Unit Spheres of Certain Banach Lattices
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