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SUB-LAPLACIAN: 作品数：11被引量：8H指数：1; 导出分析报告; 相关领域：理学自动化与计算机技术更多>>; 相关机构：广州大学更多>>; 相关期刊：《Journal of Partial Differential Equations》《Analysis in Theory and Applications》《Science China Mathematics》《Acta Mathematica Scientia》更多>>; 相关基金：国家自然科学基金中国博士后科学基金国家教育部博士点基金更多>>

A Note on the Heat Kernel for the Rescaled Harmonic Oscillator from Two Step Nilpotent Lie Groups: 《Acta Mathematica Sinica,English Series》2022年第9期1597-1611,共15页Zhi Peng YANG; Supported by the National Natural Science Foundation of China (Grant Nos.12101546,11771385)。; In this note,we use Schr?dinger representations and the Fourier transform on two step nilpotent Lie groups to compute the explicit formula of the sub-Laplacian operator and its symbol,which is associated with the resc...; 关键词：SUB-LAPLACIAN heat kernel nilpotent Lie groups

On fundamental solution for powers of the sub-Laplacian on the Heisenberg group被引量：1: 《Applied Mathematics(A Journal of Chinese Universities)》2017年第3期365-378,共14页WANG Hai-meng WU Qing-yan; Supported by Doctor Special Foundation of Jiangsu Second Normal University(JSNU2015BZ07); 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...; 关键词：SUB-LAPLACIAN fundamental solution group Fourier transform Plancherel formula Heisenberg group

Wiener measure for Heisenberg group被引量：1: 《Science China Mathematics》2014年第8期1605-1614,共10页LIU HePing WANG YingZhan; supported by National Natural Science Foundation of China (Grant No. 10990012);50-Class General Financial Grant from the China Postdoctoral Science Foundation (Grant No. 2011M501317); We build Wiener measure for the path space on the Heisenberg group by using of the heat kernel corresponding to the sub-Laplacian and give the definition of the Wiener integral.Then we give the FeynmanKac formula.; 关键词：Heisenberg group C-C distance sub-Laplacian operator Wiener measure Feynman-Kac formula

ON UNIQUE CONTINUATION PROPERTIES FOR THE SUB-LAPLACIAN ON CARNOT GROUPS: 《Acta Mathematica Scientia》2010年第5期1776-1784,共9页钮鹏程王家林; supported by the National Natural Science Foundation of China(10871157);Research Fund for the Doctoral Program of Higher Education of China(200806990032);Keji Chuangxin Jijin of Northwestern Polytechnical University(2007KJ01012); In this article, authors begin with establishing representation formulas and properties for functions on Carnot groups. Then, some unique continuation results to solutions of sub-Laplace equations with potentials are ...; 关键词：unique continuation representation formula spherical function Carnotgroup SUB-LAPLACIAN

Trace of heat kernel,spectral zeta function and isospectral problem for sub-laplacians: 《Science China Mathematics》2009年第12期2570-2589,共20页CHANG Der-Chen YEUNG Sai-Kee; supported by National Security Agency,United States Army Research Offfice and a Hong Kong RGC Competitive Earmarked Research (Grant No. 600607); In this article, we first study the trace for the heat kernel for the sub-Laplacian operator on the unit sphere in ? n+1. Then we survey some results on the spectral zeta function which is induced by the trace of the ...; 关键词：SUB-LAPLACIAN heat kernel CR-isospectral problem Riemannian zeta function Mellin transform pseudo-hermitian structure Primary: 53C17 Secondary: 34K10 35H20

Dirichlet Eigenvalue Ratios for the p-sub-Laplacian in the Carnot Group: 《Journal of Partial Differential Equations》2009年第1期1-10,共10页WEI Na NIU Pengcheng LIU Haifeng; We prove some new Hardy type inequalities on the bounded domain with smooth boundary in the Carnot group. Several estimates of the first and second Dirich- let eigenvalues for the p-sub-Laplacian are established.; 关键词：Carnot group p-sub-Laplacian Dirichlet eigenvalue Hardy-type inequality.

SOME LIOUVILLE TYPE THEOREMS FOR THE P-SUB-LAPLACIAN ON THE GROUP OF HEISENBERG TYPE: 《Journal of Partial Differential Equations》2008年第3期193-207,共15页Yuan Zixia Niu Pengcheng; In this paper we prove some Liouville type results for the p-sub-Laplacian on the group of Heisenberg type. A strong maximum principle and a Hopf type principle concerning p-sub-Laplacian are established.; 关键词：p-sub-Laplacian Liouville type theorems group of Heisenberg type Strong maximum principle.

A CARLEMAN ESTIMATE ON GROUPS OF HEISENBERG TYPE: 《Journal of Partial Differential Equations》2006年第4期341-358,共18页Han Junqiang Niu Pengcheng; The project supported by National Natural Science Foundation of China, Grant No. 10371099.; A Pohozaev-Rellich type identity for the p-sub-Laplacian on groups of Heisenberg type, G, is given. A Carleman estimate for the sub-Laplacian on G is established and, as a consequence, a unique continuation result is ...; 关键词：Pohozaev-Rellich type identity Carleman estimate unique continuation SUB-LAPLACIAN group of Heisenberg type.

A Note on Hermite and Subelliptic Operators被引量：7: 《Acta Mathematica Sinica,English Series》2005年第4期803-818,共16页Der Chen CHANG Jing Zhi TIE; partially supported by a William Fulbright Research Grant and a Competitive Research Grant at Georgetown University; In this note, we compute the fundamental solution for the Hermite operator with singularity at an arbitrary point y∈R^n. We also apply this result to obtain the fundamental solutions for the Grushin operator in R^2 a...; 关键词：Hermite operator Heisenberg group SUB-LAPLACIAN Gruhsin operator Heat kernel Laguerre function

SUB-LAPLACIANS ON A CLASS OF HOMOGENEOUS GROUPS: 《Science China Mathematics》1992年第5期561-569,共9页孙利民; An important class of homogeneous groups N(Φ) is introduced, which includes the distin-guishing boundaries of the Siegel domains of Type Ⅱ. For the sub-Laplacian ? on N(Φ),its basic eigenfunctions are obtained by a...; 关键词：HOMOGENEOUS GROUP SUB-LAPLACIAN EIGENFUNCTION foundamental solution.

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