Fundamental Solutions of Kohn Sub-Laplacians on Anisotropic Heisenberg Groups and H-type Groups
Printed: Mar 2011
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 $\alpha$ 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.
22E30 - Analysis on real and complex Lie groups [See also 33C80, 43-XX]
35R03 - Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.
43A80 - Analysis on other specific Lie groups [See also 22Exx]