• 대한수학회보
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• 제36권4호
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• pp.737-746
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• 1999

For a locally compact Abelian group G, and a commutative Banach algebra B, let $L^1$(G, B) be the Banach algebra of all Bochner integrable functions. We show that if G is noncompact and B is a semiprime Banach algebras in which every minimal prime ideal is cnotained in a regular maximal ideal, then $L^1$(G, B) contains no nontrivial separating idal. As a consequence we deduce some automatic continuity results for $L^1$(G, B).

• 대한수학회지
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• 제12권1호
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• pp.13-27
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• 1975

• 대한수학회지
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• 제14권2호
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• pp.213-215
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• 1978

• 대한수학회보
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• 제42권3호
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• pp.555-561
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• 2005

In this note we give characterizations for certain HNN extensions with central associated subgroups to be residually finite. We then apply our results to HNN extensions of polycyclic-by-finite groups.

• 충청수학회지
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• 제10권1호
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• pp.161-175
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• 1997

We classify free actions of finite abelian groups on the 3-dimensional nilmanifold, up to topological conjugacy. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal subgroups of almost Bieberbach groups of finite index, up to affine conjugacy.

• 충청수학회지
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• 제13권2호
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• pp.71-79
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• 2001

We study only free actions of finite abelian groups G on the 3-dimensional nilmanifold, up to topological conjugacy. we shall deal with only one out of 15 distinct almost Bieberbach groups up to Seifert local invariant.

• 대한수학회지
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• 제49권3호
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• pp.571-583
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• 2012

Let $G$ be a metrizable, ${\sigma}$-compact locally compact abelian group with a compact open subgroup. In this paper we define the Gramian and the dual Gramian operators for shift invariant subspaces of $L^2(G)$ and we use them to characterize shift generated dual frames for shift in- variant spaces, which forms a frame for a subspace of $L^2(G)$. We present necessary and sufficient conditions for which standard dual is a unique SG-dual frame of type I and type II.

• 대한수학회보
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• 제29권1호
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• pp.153-163
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• 1992

Carlitz module is used to study abelian extensions of K=$F_{q}$(T). In number theory every abelian etension of Q is contained in a cyclotomic field. Similarly every abelian extension of $F_{q}$(T) with some condition on .inf. is contained in a cyclotomic function field. Hence the study of cyclotomic function fields in analogy with cyclotomic fields is an important subject in number theory. Much are known in this direction such as ring of integers, class groups and units ([G], [G-R]). In this article we are concerned with the ring of integers in a cyclotomic function field. In [G], it is shown that the ring of integers is generated by a primitive root of the Carlitz module using the ramification theory and localization. Here we will give another proof, which is rather elementary and explicit, of this fact following the methods in [W].[W].

• 대한수학회지
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• 제48권5호
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• pp.899-912
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• 2011

We introduce ${\varphi}$-frames in $L^2$(G), as a generalization of a-frames defined in [8], where G is a locally compact Abelian group and ${\varphi}$ is a topological automorphism on G. We give a characterization of ${\varphi}$-frames with regard to usual frames in $L^2$(G) and show that ${\varphi}$-frames share several useful properties with frames. We define the associated ${\varphi}$-analysis and ${\varphi}$-preframe operators, with which we obtain criteria for a sequence to be a ${\varphi}$-frame or a ${\varphi}$-Bessel sequence. We also define ${\varphi}$-Riesz bases in $L^2$(G) and establish equivalent conditions for a sequence in $L^2$(G) to be a ${\varphi}$-Riesz basis.

• 대한수학회지
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• 제41권5호
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• pp.913-920
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• 2004

We give a characterization for fundamental groups of graphs of groups amalgamating cyclic edge subgroups to be cyclic subgroup separable if each pair of edge subgroups has a non-trivial intersection. We show that fundamental groups of graphs of abelian groups amalgamating cyclic edge subgroups are cyclic subgroup separable, hence residually finite, if each edge subgroup is isolated in its containing vertex group.