Bargmann transform on the space of hyperplanes

TL;DR

This paper introduces a new Bargmann transform on the space of hyperplanes using the Radon transform's Plancherel formula, linking microlocal analysis with integral geometry.

Contribution

It extends the classical Bargmann transform to hyperplanes, providing a novel framework that combines microlocal analysis and the Radon transform.

Findings

Established the Bargmann transform on hyperplanes.

Connected microlocal analysis with the Radon transform.

Provided foundational properties of the new transform.

Abstract

We introduce a Bargmann transform on the space of hyperplanes by applying the Plancherel formula of the Radon transform to the definition of the Bargmann transform on the Euclidean space. Some basic facts on microlocal analysis are also discussed.