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研究生:方婉茜
研究生(外文):Wan-Chain Fang
論文名稱:Wiener環的保分性線性泛函
論文名稱(外文):Disjointness preserving linear functionals of the Wiener ring
指導教授:黃毅青
指導教授(外文):Ngai-Ching Wong
學位類別:碩士
校院名稱:國立中山大學
系所名稱:應用數學系研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:22
中文關鍵詞:Wiener-環保分性線性泛函
外文關鍵詞:disjointness preserving linear functionalsWiener ring
相關次數:
  • 被引用被引用:0
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  • 下載下載:5
  • 收藏至我的研究室書目清單書目收藏:0
本論文探討Wiener 環的保分性線性泛函的型式。 由Gelfand轉換(亦即富利葉轉換)得到Wiener環是C(T)的稠密子代數,因而具備了C(T)的範數。然而,Wiener 環亦等價於L1(Z),所以也具備了L1範數。利用對Wiener 環理想結構的分析,我們發現兩種範數下的有界保分性線性泛函事實上是一樣的。且不管以何種角度出發,Wiener
環的保分性線性泛函都是一個點質量(point mass)的常數倍。最後,我們建立了無界的Wiener環的保分性線性泛函的存在性。
In this thesis, we shall study disjointness preserving linear functionals of the Wiener ring. It is clear that Wiener ring is a dense subalgebra of C(T)in the usual supremum norm .However, Wiener ring is also isomorphic to L1(Z). So it has an 1 norm . By studying
the structure of ideals of the Wiener ring, we discover that disjointness preserving linear functionals are the same under different norms. Bounded disjointness preserving linear functionals of the Wiener ring is a multiple of the point mass in both cases. Finally, we establish the existence of unbounded
disjointness preserving linear functionals of the Wiener ring.
1.Introduction.........................................................1
2.Notations and Preliminarles..........................................3
2.1 General theory of group algebras.................................3
2.2 some basic result of L1(Z).......................................6
3.Main results.........................................................11
3.1 Approzimating continuous functions by smooth function............11
3.2 Disjointness preserving linear functionals of the Wiener ring....17
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J. R. Munkres. Analysis on Manifolds, Addison-Wesley Publishing
Company, Redwood (1930).
L. H. Loomis. An Introduction to Abstract Harmonic Analysis,
D. Van Nostrand company, Inc., Toronto (1953).
W. Rudin. Real and Complex Analysis. Tata McGraw-Hill
Publishing Company Ltd., New Delhi (1974).
W. Rudin. Fourier Analysis on Groups. Interscience Publishers,
New York (1962).
K. Zhu. An Introduction to Operator Algebras. CRC Press,
Inc., Florida (1993).
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