Bourgain's projection theorem over normed division algebras

TL;DR

This paper extends Bourgain's projection theorem from real numbers to division algebras over local fields of zero characteristic, providing a simple and self-contained proof.

Contribution

It offers a novel extension of Bourgain's projection theorem to division algebras over local fields, with a simplified proof approach.

Findings

Extended Bourgain's projection theorem to division algebras over local fields

Provided a simple, self-contained proof of the extension

Broadens the applicability of the original theorem

Abstract

We give a simple and self-contained proof of an extension of a projection theorem of Bourgain over the reals to division algebras over local fields of zero characteristic.