• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.507-514
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• 2018

Let $\{{\varphi}_n\}_{n{\geq}1}$ be a sequence of analytic self-maps of ${\mathbb{D}}$. It is proved that if the union set of the ranges of the composition operators $C_{{\varphi}_n}$ on the weighted Bergman spaces contains the disk algebra, then ${\varphi}_k$ is an automorphism of ${\mathbb{D}}$ for some $k{\geq}1$.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.141-146
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• 1997

In this paper we prove that the corona theorem for the algebra $H^{\infty}(D){\cap}D(D)$. That is, we prove that $\mathcal{M}{\setminus}{\overline{D}}$ is an empty set where $\mathcal{M}$ is the maximal ideal space of the given algebra.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.533-542
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• 2019

We study commutants of Toeplitz operators acting on the Dirichlet space of the unit disk and prove that an operator in the Toeplitz algebra commuting with a Toeplitz operator with a nonconstant polynomial symbol must be a Toeplitz operator with an analytic symbol.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.451-459
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• 2023

We give a characterization of zero divisors of the ring C[a, b]. Using the Weierstrass approximation theorem, we completely characterize topological divisors of zero of the Banach algebra C[a, b]. We also characterize the zero divisors and topological divisors of zero in ℓ^∞. Further, we show that zero is the only zero divisor in the disk algebra 𝒜 (𝔻) and that the class of singular elements in 𝒜 (𝔻) properly contains the class of topological divisors of zero. Lastly, we construct a class of topological divisors of zero of 𝒜 (𝔻) which are not zero divisors.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.397-420
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• 2011

In this paper we study the structure of closed weakly dense ideals in Privalov spaces $N^p$ (1 < p < $\infty$) of holomorphic functions on the disk $\mathbb{D}$ : |z| < 1. The space $N^p$ with the topology given by Stoll's metric [21] becomes an F-algebra. N. Mochizuki [16] proved that a closed ideal in $N^p$ is a principal ideal generated by an inner function. Consequently, a closed subspace E of $N^p$ is invariant under multiplication by z if and only if it has the form $IN^p$ for some inner function I. We prove that if $\cal{M}$ is a closed ideal in $N^p$ that is dense in the weak topology of $N^p$, then $\cal{M}$ is generated by a singular inner function. On the other hand, if $S_{\mu}$ is a singular inner function whose associated singular measure $\mu$ has the modulus of continuity $O(t^{(p-1)/p})$, then we prove that the ideal $S_{\mu}N^p$ is weakly dense in $N^p$. Consequently, for such singular inner function $S_{\mu}$, the quotient space $N^p/S_{\mu}N^p$ is an F-space with trivial dual, and hence $N^p$ does not have the separation property.

• Journal of Korea Spatial Information System Society
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• v.4 no.1 s.7
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• pp.39-46
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• 2002

In distributed spatial database systems, users nay issue a query that joins two relations stored at different sites. The sheer volume and complexity of spatial data bring out expensive CPU and I/O costs during the spatial join processing. This paper shows a new spatial join method which joins two spatial relation in a parallel way. Firstly, the initial join operation is divided into two distinct ones by partitioning one of two participating relations based on the region. This two join operations are assigned to each sites and executed simultaneously. Finally, each intermediate result sets from the two join operations are merged to an ultimate result set. This method reduces the number of spatial objects participating in the spatial operations. It also reduces the scope and the number of scanning spatial indices. And it does not materialize the temporary results by implementing the join algebra operators using the iterator. The performance test shows that this join method can lead to efficient use in terms of buffer and disk by narrowing down the joining region and decreasing the number of spatial objects.