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A Note on Hermite and Subelliptic Operators
作者姓名:Der  Chen  CHANG  Jing  Zhi  TIE
作者单位:[1]Department of Mathematics, Georgetown University, Washington, DC 20057-1233. USA [2]Department of Mathematics, University of Georgia, Athens, GA 30602-7403, USA
基金项目:The research is partially supported by a William Fulbright Research Grant and a Competitive Research Grant at Georgetown University.
摘    要: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 and the sub-Laplacian in the Heisenberg group Hn.

关 键 词:Hermite算子  Heisenberg群  Laplacian算子  Gruhsin算子  Laguerre函数
收稿时间:2003-03-25
修稿时间:2003-03-252003-07-16

A Note on Hermite and Subelliptic Operators
Der Chen CHANG Jing Zhi TIE.A Note on Hermite and Subelliptic Operators[J].Acta Mathematica Sinica,2005,21(4):803-818.
Authors:Der Chen Chang  Jing Zhi Tie
Institution:(1) Department of Mathematics, Georgetown University, Washington, DC 20057-1233, USA;(2) Department of Mathematics, University of Georgia, Athens, GA 30602-7403, USA
Abstract: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 ℝ2 and the sub-Laplacian in the Heisenberg group H n . Dedicated to Professor Silei Wang on the occasion of his 70th brithday The research is partially supported by a William Fulbright Research Grant and a Competitive Research Grant at Georgetown University
Keywords:Hermite operator  Heisenberg group  Sub-Laplacian  Gruhsin operator  Heat kernel  Laguerre function
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