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Mathematics > Numerical Analysis

arXiv:1810.08105 (math)
[Submitted on 18 Oct 2018]

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

Authors: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.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:1810.08105 [math.NA]
  (or arXiv:1810.08105v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1810.08105
Journal reference: Anal.Math.Phys. 10, 38 (2020)
Related DOI: https://doi.org/10.1007/s13324-020-00383-2

Submission history

From: Michael Quellmalz [view email]
[v1] Thu, 18 Oct 2018 15:21:06 UTC (19 KB)
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