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

Published online by Cambridge University Press:  20 November 2018

Yongyang Jin
Affiliation:
Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, 310032, China e-mail: yongyang@zjut.edu.cn
Genkai Zhang
Affiliation:
Department of Mathematics, Chalmers University of Technology and Göteborg University, Göteborg, Sweden e-mail: genkai@chalmers.se
Corresponding
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Abstract

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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2011

References

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