On fundamental solution for powers of the sub-Laplacian on the Heisenberg group |
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| Authors: | Hai-meng Wang Qing-yan Wu |
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| Institution: | 1. School of Mathematics and Information Technology, Jiangsu Second Normal University, Nanjing 210013, China;2. School of Science, Linyi University, Linyi 276000, China |
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| Abstract: | We discuss the fundamental solution for m-th powers of the sub-Laplacian on the Heisenberg group. We use the representation theory of the Heisenberg group to analyze the associated m-th powers of the sub-Laplacian and to construct its fundamental solution. Besides, the series representation of the fundamental solution for square of the sub-Laplacian on the Heisenberg group is given and we also get the closed form of the fundamental solution for square of the sub-Laplacian on the Heisenberg group with dimension n=2,3,4. |
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| Keywords: | sub-Laplacian fundamental solution group Fourier transform Plancherel formula Heisenberg group |
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