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| 研究生： |
羅阡豪 Luo, Qian-Hao |
|---|---|
| 論文名稱： |
Fundamental Solutions on the Heisenberg Group Fundamental Solutions on the Heisenberg Group |
| 指導教授： | 陳瑞堂 |
| 學位類別： |
碩士 Master |
| 系所名稱： |
數學系 Department of Mathematics |
| 論文出版年： | 2019 |
| 畢業學年度： | 107 |
| 語文別： | 英文 |
| 論文頁數： | 32 |
| 中文關鍵詞： | CR manifold 、Heisenberg group 、fundamental solution |
| 英文關鍵詞： | CR manifold, Heisenberg group, fundamental solution |
| DOI URL： | http://doi.org/10.6345/NTNU201900006 |
| 論文種類： | 學術論文 |
| 相關次數： | 點閱：158 下載：11 |
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無中文摘要
This paper is an expository note mainly concentrated on section 2,4,5,6 and 7 of Folland and Stein's work. We first review some definitions and properties of CR manifolds, ∂ ̅_b complex and Heisenberg groups. We then derive the explicit form of the Laplacian □_b and deduce the problem of □_b to the operator L_α. The major part of the paper is to find the fundamental solutions for L_α on the Heisenberg group and to compute the constant c_α. Last we analyze the solutions of L_α f=g to finish the paper.
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