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.
|Title of host publication||Operator Theory|
|Subtitle of host publication||Advances and Applications|
|Number of pages||24|
|State||Published - 2020|
|Name||Operator Theory: Advances and Applications|
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