科研之友
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摘要
The Funk-Radon transform assigns to a function on the two-sphere its mean values along all great circles. We consider the following generalization: we replace the great circles by the small circles being the intersection of the sphere with planes containing a common point zeta inside the sphere. If zeta is the origin, this is just the classical Funk-Radon transform. We find two mappings from the sphere to itself that enable us to represent the generalized Radon transform in terms of the Funk-Radon transform. This representation is utilized to characterize the null space and range as well as to prove an inversion formula of the generalized Radon transform.
- 出版日期2017-3
