姓名 |
林淑惠(Sue-Hwi Lin)
查詢紙本館藏 |
畢業系所 |
數學系 |
論文名稱 |
關於巴氏空間上連續函數的近乎收斂性 (On almost convergence of continuous functions in Banach spaces)
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相關論文 | |
檔案 |
[Endnote RIS 格式]
[Bibtex 格式]
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摘要(中) |
這篇論文主要在研究所有值域在巴氏空間上的連續函數的近乎收斂性、強近乎收斂性、以及(C,1)收斂、C-all*收斂,得到一些新的結果。 |
摘要(英) |
This thesis is concerned with the relations between almost convergence, strongly almost convergence, convergence in (C,1) sense, convergence in C-all* sense in the space C([0,∞), X ) of all continuous function with values in Banach space X. Some counterexamples of these properties are discussed. |
關鍵字(中) |
★ 近乎收斂 ★ 巴氏空間 |
關鍵字(英) |
★ almost convergence ★ strong almost convergence |
論文目次 |
Section 1. Introduction…………………...1
Section 2. Equivalence condition for almost convergence ………………....5
Section 3. Cauchy criterions for almost
convergence and strong almost convergence………………….9
Section 4. Tauberian theorem for almost convergence………………...14
Section 5. Tauberian condition from (C,1) convergence to almost convergence………………...16
Section 6. Tauberian condition from C-all* convergence to norm convergenve………………...20
References……………………………………22 |
參考文獻 |
P. L. Butzer and R. J. Nessel,Fourier Analysis and
Approximation,Vol. 1: one-dimensional theory. Academic Press, New York-London,1971.
P. L. Butzer and R. J. Nessel,Aspects of de La Vallee-Poussin's work in approximation and its influence, Arch. Hist. Exact Sci.46(1993), no. 1,
67-95.
Meng-Kuang Kuo, Characterization of w-almost convergent double
sequences and their related properties, Ph.D. Dissertation, National
Tsing Hua University, 2004.
G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math.80(1948), 167-190.
I. J. Maddox, A new type of convergence, Math. Proc. Cambridge-Philos.
Soc.83(1978), no. 1, 61-64.
I. J. Maddox, Some general Tauberian theorems,J. London Math.Soc.(2)7(1974), 645-650. |
指導教授 |
高華隆、蕭勝彥 (Hwa-Long Gau、Sen-Yen Shaw)
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審核日期 |
2005-7-5 |
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