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

Jin, Yongyang ; Zhang, Genkai

Canadian mathematical bulletin, Tome 54 (2011) no. 1, pp. 126-140

Résumé

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.

Détail

DOI : 10.4153/CMB-2010-086-1

Mots-clés : 22E30, 35R03, 43A80

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