On the Spherical Slice Transform

2021/01/17 by Boris Rubin, Rubin, Boris
Mathematics · #44A12 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:44A12

paper · pdf · doi:10.48550/arxiv.2101.06783

16 pages, 2 figures

arxiv created 2021/08/01 · arxiv updated 2021/08/03

Abstract

We study the spherical slice transform which assigns to a function on the n-dimensional unit sphere the integrals of that function over cross-sections of the sphere by k-dimensional affine planes passing through the north pole. These transforms are well known when k=n. We consider all 1< k < n+1 and obtain an explicit formula connecting the spherical slice transform with the classical Radon-John transform over (k-1)-dimensional planes in the n-dimensional Euclidean space. Using this connection, known facts for the Radon-John transform, like inversion formulas, support theorems, representation on zonal functions, and others, can be reformulated for the spherical slice transform.

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