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研究生: 盧欽昌
Cin-Chang Lu
論文名稱: 歐氏空間單位球上有界調和函數的支配現象
Dominating phenomenon for bounded real harmonic functions in the unit ball
指導教授: 程守慶
So-Chin Chen
口試委員:
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: 2008
畢業學年度: 96
語文別: 英文
論文頁數: 21
中文關鍵詞: 支配現象解析函數
外文關鍵詞: Dominating phenomenon, holomorphic function
相關次數: 點閱:3下載:0
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  • 在此篇文章當中, 我們循著當年Brown, Shield 以及 Zeller 的思路, 在高維度的複球上探討關於有界解析函數(bounded holomorphic function)的邊界行為. 在過程中我們也對歐氏空間單位球上實數值有界調和函數以及實數值有界M-調和函數的支配現象作初步的探討


    In this article, following the line developed by Brown, Shields and Zeller, we
    study the nontangential behavior of holomorphic functions in the unit ball Bn
    of Cn: The dominating phenomenon for real bounded harmonic functions in the
    unit ball Bn of Rn and M-harmonic functions in the unit ball Bn of Cn are also
    investigated.

    Contents 1 Introduction 2 2 Preliminary results 3 2.1 An auxiliary lemma. . . . . . 3 2.2 Some background from Functional and Complex Analysis 4 3 The Banach space E(Bn) 6 3.1 Main result . . . . . . . . . . . . . . . . . 6 3.2 Some examples . . . . . . . . . . . . . . . 11 4 Dominating sets for bounded harmonic functions on Bn in Rn 13 5 Dominating sets for bounded M-harmonic functions on Bn of Cn 17 5.1 K-Limit . . . . . . . . . . . . . . . . . . . . . . . 17 5.2 M-harmonic functions . . . . . . . . . . . . . . . 17

    References
    [1] F. F. Bonsall, Domination of the supremum of a bounded harmonic function by
    its supremum over a countable subset, Proceeding of the Edinburgh Mathematical
    Society. 30, 471-477(1987).
    [2] L. Brown, A. Shields and K. Zeller, On absolutely convergent exponential sums,
    Trans. Amer. Math. Soc. 96, 162-183(1960).
    [3] J. B. Conway, A Course in Functional Analysis, Springer-Verlag, New York, 1990.
    [4] E. Hille and R. S. Phillips, Functional analysis and semi-groups, Amer. Math. Soc.
    Colloquium Publications, vol. 31, 1957.
    [5] S. G. Krantz, Function theory of several complex variables, AMS Chelsea Publish-
    ing, 2000.
    [6] R. Narasimhan, Several complex variables, University of Chicago, 1971.
    [7] W. Rudin, Function theory in the unit ball of Cn; Springer-Verlag, New York, 1980.
    [8] W. Rudin, Real and complex analysis, McGraw-Hill, 1987.

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