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| 研究生： |
謝詠傑 Hsieh, Yung-Chieh |
|---|---|
| 論文名稱： |
多維複空間中環形圓域之擬凸性與多項式凸性 On pseudoconvexity and polynomial convexity of torus-like domains in C^n |
| 指導教授： |
程守慶
Chen, So-Chin |
| 口試委員: |
李大中
Lee, Ta-Chung 李華倫 Li, Hua-Lun |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系 Department of Mathematics |
| 論文出版年： | 2018 |
| 畢業學年度： | 106 |
| 語文別： | 英文 |
| 論文頁數： | 13 |
| 中文關鍵詞： | 環形圓域 、擬凸性 、多項式凸性 、多重次調和 |
| 外文關鍵詞： | torus-like domain, pseudoconvexity, polynomial convexity, plurisubharmonic |
| 相關次數： | 點閱：2 下載：0 |
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本論文首先於多維複空間中定義兩種環形圓域：Tc 與 TR。接著針對所有可能的小球半徑，探討這兩種環形圓域的擬凸性與多項式凸性。
In this thesis, two kinds of open solid tori (or torus-like domains) in C^n, n greater than or equal to 2, Tc and TR are defined. Also, the pseudoconvexity and polynomial convexity of Tc and TR are investigated for all possible radii of minor spheres.
1. R. M. Range, Holomorphic Functions and Integral Representations in Several Complex Variables, Graduate Texts in Mathematics, Vol. 108. Springer-Verlag, New York, 1986.
2. E. L. Stout, Polynomial Convexity, Prog. Math., Vol.261, Birkhauser, Boston, 2007.
3. L. V. Hormander, An Introduction to Complex Analysis in Several Variables, D. Van Nostrand, Princeton, Toronto, London, 1966.
4. E. Kallin, Polynomial convexity: The three spheres problem, Conference on Complex Analysis Held in Minneapolis, 1964, Springer-Verlag, Berlin, 1965, pp. 301-304.
5. S. Krantz, Function Theory of Several Complex Variables, second edition, Wadsworth, Pacific Grove, 1992.
6. G. M. Henkin, Integral representations of functions holomorphic in strictly pseudoconvex domain and some applications, Math. USSR. Sb. 7, 1969, pp. 597-616.