# Roe- Strichartz Theorem on Two Step Nilpotent Lie Groups

## TL;DR

This paper extends Roe-Strichartz eigenfunction characterization from Euclidean and Heisenberg groups to a broader class of two-step nilpotent Lie groups, advancing understanding of harmonic analysis on these structures.

## Contribution

It generalizes the Roe-Strichartz theorem to connected, simply connected two-step nilpotent Lie groups, broadening the scope of eigenfunction characterization.

## Key findings

- Eigenfunctions characterized by boundedness conditions on two-step nilpotent Lie groups
- Extension of Roe-Strichartz theorem beyond Euclidean and Heisenberg groups
- Advancement in harmonic analysis on nilpotent Lie groups

## Abstract

Strichartz characterized eigenfunctions of the Laplacian on Euclidean spaces by boundedness conditions which generalized a result of Roe for the one-dimensional case. He also proved an analogous statement for the sublaplacian on the Heisenberg groups. In this paper, we extend this result to connected, simply connected two step nilpotent Lie groups.