Fourier–Wigner transforms and Liouville's theorems for the sub-Laplacian on the Heisenberg group
Volume 88 / 2010
Banach Center Publications 88 (2010), 67-75
MSC: Primary 47F05, 47G30; Secondary 35H20.
DOI: 10.4064/bc88-0-6
Abstract
The sub-Laplacian on the Heisenberg group is first decomposed into twisted Laplacians parametrized by Planck's constant. Using Fourier–Wigner transforms so parametrized, we prove that the twisted Laplacians are globally hypoelliptic in the setting of tempered distributions. This result on global hypoellipticity is then used to obtain Liouville's theorems for harmonic functions for the sub-Laplacian on the Heisenberg group.
