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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