| A Note on Hermite and Subelliptic Operators |
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| 引用本文： | Der Chen CHANG Jing Zhi TIE. A Note on Hermite and Subelliptic Operators[J]. 数学学报(英文版), 2005, 21(4): 803-818. DOI: 10.1007/s10114-004-0336-0 |
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| 作者姓名： | Der Chen CHANG Jing Zhi TIE |
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| 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 |
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| 基金项目： | The research is partially supported by a William Fulbright Research Grant and a Competitive Research Grant at Georgetown University. |
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| 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.
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| 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 |
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| Der Chen Chang,Jing Zhi Tie. A Note on Hermite and Subelliptic Operators[J]. Acta Mathematica Sinica(English Series), 2005, 21(4): 803-818. DOI: 10.1007/s10114-004-0336-0 |
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| Authors: | Der Chen Chang Jing Zhi Tie |
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| Affiliation: | (1) Department of Mathematics, Georgetown University, Washington, DC 20057-1233, USA;(2) Department of Mathematics, University of Georgia, Athens, GA 30602-7403, USA |
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| 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 |
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| Keywords: | Hermite operator Heisenberg group Sub-Laplacian Gruhsin operator Heat kernel Laguerre function |
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