Abstract
We study non-geodesic Funk-type transforms on the unit sphere 𝕊n in ℝn+1 associated with cross-sections of 𝕊n by k-dimensional planes passing through an arbitrary fixed point inside the sphere. The main results include injectivity conditions for these transforms, inversion formulas, and connection with geodesic Funk transforms. We also show that, unlike the case of planes through a single common center, the integrals over spherical sections by planes through two distinct centers provide the corresponding reconstruction problem a unique solution.
Dedicated to Professor Nikolai Vasilevski on the occasion of his 70th anniversary
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The authors are thankful to the referee for his valuable remarks and suggestions.
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Agranovsky, M., Rubin, B. (2020). Non-geodesic Spherical Funk Transforms with One and Two Centers. In: Bauer, W., Duduchava, R., Grudsky, S., Kaashoek, M. (eds) Operator Algebras, Toeplitz Operators and Related Topics. Operator Theory: Advances and Applications, vol 279. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-44651-2_7
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