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Roe–Strichartz theorem on two-step nilpotent Lie groupsa |
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| Authors: | Sayan Bagchi Ashisha Kumar Suparna Sen |
| Institution: | 1. Department of Mathematics and Statistics, Indian Institute of Science Education and Research, Kolkata, Mohanpur, West Bengal, India;2. Discipline of Mathematics, Indian Institute of Technology Indore, Simrol, Indore, India;3. Department of Pure Mathematics, University of Calcutta, Kolkata, India |
| 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 sub-Laplacian on the Heisenberg groups. In this paper, we extend this result to connected, simply connected two-step nilpotent Lie groups. |
| Keywords: | eigenfunction sub-Laplacian two-step nilpotent Lie group |