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

作     者：WANG Hai-meng WU Qing-yan 

作者机构：School of Mathematics and Information Technology Jiangsu Second Normal University School of Science Linyi University 

出 版 物：《Applied Mathematics(A Journal of Chinese Universities)》 (高校应用数学学报（英文版）（B辑）)

年 卷 期：2017年第32卷第3期

页      面：365-378页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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

主　　题：sub-Laplacian fundamental solution group Fourier transform Plancherel formula Heisenberg group 

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.