Affiliation:
1. Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA
Abstract
We study the spherical slice transform [Formula: see text] which assigns to a function [Formula: see text] on the unit sphere [Formula: see text] in [Formula: see text] the integrals of [Formula: see text] over cross-sections of [Formula: see text] by [Formula: see text]-dimensional affine planes passing through the north pole [Formula: see text]. These transforms are known when [Formula: see text]. We consider all [Formula: see text] and obtain an explicit formula connecting [Formula: see text] with the classical [Formula: see text]-plane Radon–John transform [Formula: see text] on [Formula: see text]. Using this connection, known facts for [Formula: see text], like inversion formulas, support theorems, representation on zonal functions, and some others, are reformulated for [Formula: see text].
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Analysis
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献