| Issue |
Math. Model. Nat. Phenom.
Volume 13, Number 4, 2018
Harmonic analysis
|
|
|---|---|---|
| Article Number | 38 | |
| Number of page(s) | 14 | |
| DOI | https://doi.org/10.1051/mmnp/2018030 | |
| Published online | 13 September 2018 | |
Heat kernels and Green functions of sub-Laplacians on Heisenberg groups with multi-dimensional center★
1
Department of Mathematics, Institute for Advanced Studies in Basic Sciences,
Gava Zang P.O. Box 45195-1159,
Zanjan
45137-66731, Iran
2
Department of Mathematics and Statistics, York University,
4700 Keele Street,
Ontario,
Toronto
M3J 1P3, Canada
* Corresponding author: smollaha@gmail.com
Received:
5
November
2017
Accepted:
31
January
2018
We compute the sub-Laplacian on the Heisenberg group with multi-dimensional center. By taking the inverse Fourier transform with respect to the center, we get the parametrized twisted Laplacians. Then by means of the special Hermite functions, we find the eigenfunctions and the eigenvalues of the twisted Laplacians. The explicit formulas for the heat kernels and Green functions of the twisted Laplacians can then be obtained. Then we give an explicit formula for the heat kernal and Green function of the sub-Laplacian on the Heisenberg group with multi-dimensional center.
Mathematics Subject Classification: 47G30
Key words: Heisenberg group with multi-dimensional center / sub-Laplacian / twisted Laplacians / λ-Wigner transforms / λ-Weyl transforms / heat kernels / Green functions.
© EDP Sciences, 2018
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