The Funk-Radon transform for hyperplane sections through a common point
arXiv:1810.08105 · doi:10.1007/s13324-020-00383-2
Abstract
The Funk-Radon transform, also known as the spherical Radon transform, assigns to a function on the sphere its mean values along all great circles. Since its invention by Paul Funk in 1911, the Funk-Radon transform has been generalized to other families of circles as well as to higher dimensions. We are particularly interested in the following generalization: we consider the intersections of the sphere with hyperplanes containing a common point inside the sphere. If this point is the origin, this is the same as the aforementioned Funk--Radon transform. We give an injectivity result and a range characterization of this generalized Radon transform by finding a relation with the classical Funk--Radon transform.
References in corpus (1)
Cited by in corpus (5)
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- Approximation properties of the double Fourier sphere method
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- Injectivity of pairs of non-central Funk transforms
- A Support Characterization for Functions on the Unit Sphere with Vanishing Integrals Arising from Tangent Planes to a Given Surface