By decomposing the Laplacian on the Heisenberg group into a family of parametrized partial differential operators Lτ,τ ∈ ℝ \ {0}, and using parametrized Fourier-Wigner transforms, we give formulas and estimates for the strongly continuous one-parameter semigroup generated by Lτ, and the inverse of Lτ. Using these formulas and estimates, we obtain Sobolev estimates for the one-parameter semigroup and the inverse of the Laplacian.
@article{1393,
title = {The Semigroup and the Inverse of the Laplacian on the Heisenberg Group},
journal = {CUBO, A Mathematical Journal},
volume = {12},
year = {2010},
language = {en},
url = {http://dml.mathdoc.fr/item/1393}
}
Dasgupta, Aparajita; Wong, M.W. The Semigroup and the Inverse of the Laplacian on the Heisenberg Group. CUBO, A Mathematical Journal, Tome 12 (2010) . http://gdmltest.u-ga.fr/item/1393/