Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-28T10:31:15.664Z Has data issue: false hasContentIssue false
  • English
  • Français

Radon transforms of projection functions

Published online by Cambridge University Press:  01 January 1998

PAUL GOODEY
PAUL GOODEY
Affiliation:
Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that a centrally symmetric convex body is determined, up to translation, by any Radon transform of one of its projection functions. It is also proved that all Radon transforms are injective when restricted to projection functions of polytopes. Both results were known previously in the case of Radon transforms Ri,j with i<j. Here we use harmonic analysis on Grassmann manifolds to show that these results extend to all Radon transforms.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 123 , Issue 1 , January 1998 , pp. 159 - 168
Copyright
Cambridge Philosophical Society 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)