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

被引：0

作者：

WANG Haimeng ^{[1
]}

WU Qingyan ^{[2
]}

机构：

[1] School of Mathematics and Information Technology, Jiangsu Second Normal University

[2] School of Science, Linyi University

来源：

AppliedMathematics:AJournalofChineseUniversities | 2017年 / 32卷 / 03期

关键词：

sub-Laplacian; fundamental solution; group Fourier transform; Plancherel formula; Heisenberg group;

D O I：

暂无

中图分类号：

O177 [泛函分析];

学科分类号：

070104 ;

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.

引用

页码：365 / 378

页数：14

共 13 条

[1] 一般二步幂零群上Laplacian算子的基本解 [J].

王海蒙 ;

谢非非 .

高校应用数学学报A辑, 2013, 28 (03) :347-358

[2] Laguerre calculus and Paneitz operator on the Heisenberg group [J].

Chang Der-Chen ;

Chang Shu-Cheng ;

Tie JingZhi .

SCIENCE IN CHINA SERIES A-MATHEMATICS, 2009, 52 (12) :2549-2569

[3]

A Note on Hermite and Subelliptic Operators[J]. Der Chen CHANG Department of Mathematics.Georgetown University,Washington,DC 20057-1233.USA Jing Zhi TIE Department of Mathematics.University of Georgia,Athens,GA 30602-7403.USA.Acta Mathematica Sinica(English Series). 2005(04)

[4]

On Octonionic Regular Functions and the Szeg? Projection on the Octonionic Heisenberg Group[J] . Haimeng Wang,Wei Wang.Complex Analysis and Operator Theory . 2014 (6)

[5]

The tangential Cauchy–Fueter complex on the quaternionic Heisenberg group[J] . Wei Wang.Journal of Geometry and Physics . 2010 (1)

[6]

The k -Cauchy–Fueter complex, Penrose transformation and Hartogs phenomenon for quaternionic k -regular functions[J] . Wei Wang.Journal of Geometry and Physics . 2009 (3)

[7] Analysis of the Kohn Laplacian on quadratic CR manifolds [J].

Peloso, MM ;

Ricci, F .

JOURNAL OF FUNCTIONAL ANALYSIS, 2003, 203 (02) :321-355

[8] Estimates for powers of sub-Laplacian on the non-isotropic Heisenberg group [J].

Der-Chen Chang ;

Jingzhi Tie .

The Journal of Geometric Analysis, 2000, 10 (4)

[9] The green function of model step two hypoelliptic operators and the analysis of certain tangential cauchy Riemann complexes [J].

Beals, R ;

Gaveau, B ;

Greiner, P .

ADVANCES IN MATHEMATICS, 1996, 121 (02) :288-345

[10]

The solution of the $$\overline \partial $$ -Neumann problem in a strictly pseudoconvex Siegel domain[J] . Nancy K. Stanton.Inventiones Mathematicae . 1981 (1)

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