• Kyungpook Mathematical Journal
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• 제61권2호
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• pp.371-381
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• 2021

In this paper, we attempt to obtain sufficient conditions for the existence of tight wavelet frame sets in locally compact abelian groups. The condition is generated by modulating a collection of characteristic functions that correspond to a generalized shift-invariant system via the Fourier transform. We present two approaches (for stationary and non-stationary wavelets) to construct the scaling function for L²(G) and, using the scaling function, we construct an orthonormal wavelet basis for L²(G). We propose an open problem related to the extension principle for Riesz wavelets in locally compact abelian groups.

• 대한수학회보
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• 제38권1호
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• pp.7-16
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• 2001

We study the Fourier transformation on the Gelfand-Bruhat space of type S and characterize this space by means of Fourier transform on a locally compact abelian group G. Also, we extend Bochner-Schwartz theorem to the dual space of the Gelfand-Bruhat space and the space of Fourier hyperfunctions on G. respectively.

• 대한수학회보
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• 제39권2호
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• pp.199-209
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• 2002

In this paper, we investigate the problem of stability of the quadratic functional equation f(x+y+z)+f(y-z)+f(y-z)+f(x-z) = 3f(x)+3f(y)+3f(z) on abelian group.

• 대한수학회보
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• 제42권1호
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• pp.53-56
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• 2005

Suppose G is a semi-complete abelian p-group and FG ${\cong}$ FH as commutative unitary F-algebras of characteristic p for any fixed group H. Then, it is shown that, G ${\cong}$ H. This improves a result of the author proved in the Proceedings of the American Math. Society (2002) and also completely solves by an another method a long-standing problem of W. May posed in the same Proceedings (1979).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권4호
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• pp.353-364
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• 2008

The purpose of this paper is to investigate the finite extension of weighted word L-delta groups. The paper revealed that a finite extension of a weighted word L-delta group is a weighted word L-delta group, and an abelian group, in addition, is a weighted word L-delta group and simultaneously a word L-delta group.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.795-805
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• 2022

The aim of author's in this paper is to study the Cayley graph in the realm of signed graph. Moreover, we have characterized generating sets and finite abelian groups that corresponds to balanced Cayley signed graphs. The notion of Cayley signed graph has been demonstrated with the ample number of examples.

• 대한수학회보
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• 제56권2호
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• pp.365-371
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• 2019

If 𝖃 is a class of groups, denote by F𝖃 the class of groups G such that for every $x{\in}G$, there exists a normal subgroup of finite index H(x) such that ${\langle}x,h{\rangle}{\in}$ 𝖃 for every $h{\in}H(x)$. In this paper, we consider the class F𝖃, when 𝖃 is the class of nilpotent-by-finite, finite-by-nilpotent and periodic-by-nilpotent groups. We will prove that for the above classes 𝖃 we have that a finitely generated hyper-(Abelian-by-finite) group in F𝖃 belongs to 𝖃. As a consequence of these results, we prove that when the nilpotency class of the subgroups (or quotients) of the subgroups ${\langle}x,h{\rangle}$ are bounded by a given positive integer k, then the nilpotency class of the corresponding subgroup (or quotient) of G is bounded by a positive integer c depending only on k.

• Kyungpook Mathematical Journal
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• 제18권1호
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• pp.11-15
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• 1978

• 대한수학회논문집
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• 제22권2호
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• pp.157-161
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• 2007

Let G be a p-mixed abelian group with semi-complete torsion subgroup $G_t$ such that G is splitting or is of torsion-free rank one, and let R be a commutative unitary ring of prime characteristic p. It is proved that the group algebras RG and RH are R-isomorphic for any group H if and only if G and H are isomorphic. This isomorphism relationship extends our earlier results in (Southeast Asian Bull. Math., 2002), (Proc. Amer. Math. Soc., 2002) and (Bull. Korean Math. Soc., 2005) as well as completely settles a problem posed by W. May in (Proc. Amer. Math. Soc., 1979).

• 대한수학회지
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• 제40권3호
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• pp.487-501
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• 2003

The paper is devoted to the description of changes of the structure of the holomorphic automorphism group of a bounded domain in \mathbb{C}^n under small perturbation of this domain in the Hausdorff metric. We consider a number of examples when an arbitrary small perturbation can lead to a domain with a larger group, present theorems concerning upper semicontinuity property of some invariants of automorphism groups. We also prove that the dimension of an abelian subgroup of the automorphism group of a bounded domain in \mathbb{C}^n does not exceed n.