Roe- Strichartz Theorem on Two Step Nilpotent Lie Groups

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.