Fourier-Wigner transforms and Liouville's theorems for the sub-Laplacian on the Heisenberg group

Aparajita Dasgupta, and M. W. Wong. "Fourier-Wigner transforms and Liouville's theorems for the sub-Laplacian on the Heisenberg group." Banach Center Publications 88.1 (2010): 67-75. <http://eudml.org/doc/282059>.

@article{AparajitaDasgupta2010,
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.},
author = {Aparajita Dasgupta, M. W. Wong},
journal = {Banach Center Publications},
keywords = {Heisenberg group; sub-Laplacian; twisted convolution; global hypoellipticity; Liouville's theorem},
language = {eng},
number = {1},
pages = {67-75},
title = {Fourier-Wigner transforms and Liouville's theorems for the sub-Laplacian on the Heisenberg group},
url = {http://eudml.org/doc/282059},
volume = {88},
year = {2010},
}

TY - JOUR
AU - Aparajita Dasgupta
AU - M. W. Wong
TI - Fourier-Wigner transforms and Liouville's theorems for the sub-Laplacian on the Heisenberg group
JO - Banach Center Publications
PY - 2010
VL - 88
IS - 1
SP - 67
EP - 75
AB - 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.
LA - eng
KW - Heisenberg group; sub-Laplacian; twisted convolution; global hypoellipticity; Liouville's theorem
UR - http://eudml.org/doc/282059
ER -