An extension of a result by Lonke to intersection bodies

TL;DR

This paper extends Lonke's result by proving that intersection bodies cannot be expressed as direct sums, and establishes necessary conditions for bodies of revolution to be intersection bodies.

Contribution

It generalizes Lonke's theorem using Fourier analysis and introduces regularity and convexity conditions for bodies of revolution as intersection bodies.

Findings

Intersection bodies cannot be direct sums.

Necessary regularity condition for bodies of revolution.

Convexity condition for bodies of revolution.

Abstract

In this paper we prove that intersection bodies cannot be direct sums using Fourier analytic techniques. This extends a result by Lonke. We also prove a necessary regularity condition and a convexity condition for a body of revolution to be an intersection body of a star body.