The semigroup and the inverse of the Laplacian on the Heisenberg group
Author
Dasgupta, Aparajita
Wong, M.W.
Full text
https://revistas.ufro.cl/ojs/index.php/cubo/article/view/139310.4067/S0719-06462010000300006
Abstract
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.