On fundamental solution for powers of the sub-Laplacian on the Heisenberg group  

作　　者：WANG Hai-meng WU Qing-yan 

机构地区：[1]School of Mathematics and Information Technology, Jiangsu Second Normal University [2]School of Science, Linyi University

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2017年第3期365-378,共14页高校应用数学学报（英文版）（B辑）

基　　金：Supported by Doctor Special Foundation of Jiangsu Second Normal University(JSNU2015BZ07)

摘　　要：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.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.

关 键 词：SUB-LAPLACIAN fundamental solution group Fourier transform Plancherel formula Heisenberg group 

分 类 号：O177[理学—数学]