Weyl Transform on Nonunimodular Groups

TL;DR

This paper investigates the unboundedness of the Weyl transform on nonunimodular groups such as the affine, similitude, and affine Poincaré groups, extending previous results from Euclidean spaces.

Contribution

It extends the study of Weyl transform unboundedness from Euclidean spaces to certain nonunimodular groups, providing new insights into their harmonic analysis.

Findings

Unboundedness of Weyl transform on affine group

Unboundedness on similitude group

Unboundedness on affine Poincaré group

Abstract

For $p>2$, B. Simon\cite{Simon} studied the unboundedness of the Weyl transform for symbol belonging to $L^p({\mathbb{R}^n\times \mathbb{R}^n})$. In this article, we study the analog of unboundedness of the Weyl transform on some nonunimodular groups, namely, the affine group, similitude group, and affine Poincar\'e group.