Fundamental Solutions of Kohn Sub-Laplacians on Anisotropic Heisenberg Groups and H-type Groups

Abstract

AbstractWe prove that the fundamental solutions of Kohn sub-LaplaciansΔ+iα∂ton the anisotropic Heisenberg groups are tempered distributions and have meromorphic continuation in α with simple poles. We compute the residues and find the partial fundamental solutions at the poles. We also find formulas for the fundamental solutions for some matrix-valued Kohn type sub-Laplacians on H-type groups.