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...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.展开更多
In this note we obtain some theorems for the well-posed initial value problem of a class of partial differential equations on the Heisenberg group H_n by means of the group Fourier transform, and therefore derive the ...In this note we obtain some theorems for the well-posed initial value problem of a class of partial differential equations on the Heisenberg group H_n by means of the group Fourier transform, and therefore derive the formulas for the fundamental solutions of the operators and with the (generalized)Kohn-Laplacian defined by an arbitrary Hermitian metric with respect to CR structure.展开更多
基金Supported by Doctor Special Foundation of Jiangsu Second Normal University(JSNU2015BZ07)
文摘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.
基金Project supported by the National Natural Science Foundation of China.
文摘In this note we obtain some theorems for the well-posed initial value problem of a class of partial differential equations on the Heisenberg group H_n by means of the group Fourier transform, and therefore derive the formulas for the fundamental solutions of the operators and with the (generalized)Kohn-Laplacian defined by an arbitrary Hermitian metric with respect to CR structure.
