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Markina, Irina
2017.
Analytic, Algebraic and Geometric Aspects of Differential Equations.
p.
89.
Published online by Cambridge University Press: 20 November 2018
We prove that the fundamental solutions of Kohn sub-Laplacians$\Delta +i\alpha {{\partial }_{t}}$ on 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 $\text{H}$-type groups.