Overdetermined transforms in integral geometry

Document Type

Article

Publication Date

1-1-2015

Abstract

We consider an example of the Gelfand-Gindikin n-dimensional complex of k-dimensional planes in Rn. Sharp existence conditions and inversion formulas are obtained for the corresponding restricted k-plane transform of Lp functions. Similar results are obtained for overdetermined Radon type transforms on the sphere and the hyperbolic space. A topological isomor-phism of the relevant Schwartz spaces with respect to the restricted k-plane transform is established. Related open problems, in particular, the restricted lower dimensional Busemann-Petty problem for sections of convex bodies, are discussed.

Publication Source (Journal or Book title)

Contemporary Mathematics

First Page

291

Last Page

313

This document is currently not available here.

Share

COinS