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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-6,
author = {Aparajita Dasgupta and M. W. Wong},
title = {Fourier-Wigner transforms and Liouville's theorems for the sub-Laplacian on the Heisenberg group},
journal = {Banach Center Publications},
volume = {89},
year = {2010},
pages = {67-75},
zbl = {1206.43006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-6}
}
Aparajita Dasgupta; M. W. Wong. Fourier-Wigner transforms and Liouville's theorems for the sub-Laplacian on the Heisenberg group. Banach Center Publications, Tome 89 (2010) pp. 67-75. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc88-0-6/