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arXiv · 1810.08105

The Funk-Radon transform for hyperplane sections through a common point

Michael Quellmalz
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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.

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Michael Quellmalz. 2018-10-18. The Funk-Radon transform for hyperplane sections through a common point. https://doi.org/10.1007/s13324-020-00383-2

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