A Restriction Theorem for M\'etivier Groups

TL;DR

This paper establishes a restriction theorem for a class of two-step nilpotent Lie groups, extending previous results on the Heisenberg group and broadening the understanding of harmonic analysis on these structures.

Contribution

It introduces a new restriction theorem applicable to certain two-step nilpotent Lie groups, generalizing M"uller's earlier work on the Heisenberg group.

Findings

Proves a restriction theorem for a class of two-step nilpotent Lie groups.

Extends M"uller's results from the Heisenberg group to broader groups.

Enhances the theoretical framework of harmonic analysis on nilpotent Lie groups.

Abstract

In the spirit of an earlier result of M\"uller on the Heisenberg group we prove a restriction theorem on a certain class of two step nilpotent Lie groups. Our result extends that of M\"uller also in the framework of the Heisenberg group.