The vertical slice transform on the unit sphere
Document Type
Article
Publication Date
8-1-2019
Abstract
The vertical slice transform in spherical integral geometry takes a function on the unit sphere Sn to integrals of that function over spherical slices parallel to the last coordinate axis. This transform was investigated for n = 2 in connection with inverse problems of spherical tomography. The present article gives a survey of some methods which were originally developed for the Radon transform, hypersingular integrals, and the spherical mean Radon-like transforms, and can be adapted to obtain new inversion formulas and singular value decompositions for the vertical slice transform in the general case n ≥ 2 for a large class of functions.
Publication Source (Journal or Book title)
Fractional Calculus and Applied Analysis
First Page
899
Last Page
917
Recommended Citation
Rubin, B. (2019). The vertical slice transform on the unit sphere. Fractional Calculus and Applied Analysis, 22 (4), 899-917. https://doi.org/10.1515/fca-2019-0049