2013 | OriginalPaper | Buchkapitel
The Heat Kernel and Green Function of a Sub-Laplacian on the Hierarchical Heisenberg Group
verfasst von : Shahla Molahajloo, M. W. Wong
Erschienen in: Pseudo-Differential Operators, Generalized Functions and Asymptotics
Verlag: Springer Basel
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We give the hierarchical Heisenberg group underpinning the hierarchical twisted Laplacian discovered recently. This hierarchical twisted Laplacian is obtained by taking the inverse Fourier transform of a sub-Laplacian with respect to a subcenter of the hierarchical Heisenberg group. Using parametrized versions of Wigner transforms and Weyl transforms, we give formulas for the heat kernels and Green functions of the parametrized hierarchical twisted Laplacians. Taking the Fourier transform of the parametrized heat kernels so obtained, we give explicit formulas for the heat kernel and Green function of the hierarchical sub-Laplacian on the hierarchical Heisenberg group.