Roe- Strichartz Theorem on Two Step Nilpotent Lie Groups

2019/06/08 by Sayan Bagchi, Bagchi, Sayan, Ashisha Kumar +3
Mathematics · #43A80 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 22E25 #Secondary 22E30 #math.FA #msc:22E25 #msc:22E30 #msc:43A80

paper · pdf · doi:10.48550/arxiv.1906.03446

arxiv created 2019/06/08 · arxiv updated 2019/06/11

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.

Related

• Lower bound of Riesz transform kernels and Commutator Theorems on stratified nilpotent Lie groups
• Improved Ingham-type result on \mathbb R^d and on connected, simply connected nilpotent Lie Groups
• On Freiman's Theorem in Nilpotent Groups
• On the sharpness of Strichartz estimates and spectrum of compact Lie groups
• Some remarks on semi-classical analysis on two-step Nilmanifolds