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研究生: 王雅楨
Wang, Ya-Cheng.
論文名稱: 多維複空間中緊緻集合多項式凸性的研究: 凱琳引理的一些應用
On polynomial convexity of compact sets in C^n: Some applications of Kallin's lemma
指導教授: 程守慶
Chen, So-Chin.
口試委員: 李大中
Lee, Tai-Chung
康素珍
Kan, Su-Jen
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: 2017
畢業學年度: 105
語文別: 英文
論文頁數: 17
中文關鍵詞: 多項式凸性多複變複分析均勻逼近
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  • 應用凱琳引理,討論多複變空間中緊緻集合的多項式凸性。如n維度複數空間中有限多個球、2維度複數空間中3個分離多圓盤、2維度複數空間中四面體之稜及n維度複數空間中的樹。


    We discuss the polynomial convexity of compact sets in C^n by applying Kallin’s separation lemma. For example, finite number of balls in C^n, 3 disjoint polydiscs in C^2, edges of tetrahedron in C^2 and trees.

    1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1 Balls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Polydiscs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.3 Tetrahedron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.4 Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

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    3. E.L. Stout,Polynomial Convexity, Birkhauser ,U.S.A, 2007.

    4. T.W. Gamelin, Uniform Algebras, Prentice Hall,Los Angeles,1969.
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    7.W. Rudin, Real and complex analysis, McGraw-Hill book company, Singapore, 1987.
    8. A.M. Kytmanov and G. Khudaiberganov, Example of a nonpolynomially convex compactum consisting of three nonintersecting ellipsoids, Sibirsk. Mat. Zh. 25 (1984), no. 5, pp.196-198.
    9.J.P. Rosay, The polynomial hull of nonconnected tube domains, and an example of E. Kallin, Bull. London Math. Soc. 21 (1989), 73-78.
    10. G. Chartrand and P. Zhang, Introduction to Graph Theory, McGraw-Hill, New York, 2005, pp.3 and pp.23.

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