• Korean Journal of Mathematics
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• v.20 no.4
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• pp.485-491
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• 2012

In this paper, we show the norm attaining paranormal operators have a nontrivial invariant subspace. Also, we show the norm attaining quadratically hyponormal weighted shift is subnormal.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.139-151
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• 2012

In the previous paper, we gave a characterization of backward shift invariant subspaces of the Hardy space over the bidisk on which [${S_z}^n$, $S_w^*$] = 0 for a positive integer n ${\geq}$ 2. In this case, it holds that ${S_z}^n=cI$ for some $c{\in}\mathbb{C}$. In this paper, it is proved that if [$S_{\varphi}$, $S_w^*$] = 0 and ${\varphi}{\in}H^{\infty}({\Gamma}_z)$, then $S_{\varphi}=cI$ for some $c{\in}\mathbb{C}$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1229-1236
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• 2009

We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator S$_K$ on a vector-valued Hardy space H$^2$(${\Omega}$, K) is generated by a quasi-inner function, we also provide relationships of quasi-inner functions by comparing rationally invariant subspaces generated by them. Furthermore, we discuss fundamental properties of quasi-inner functions and quasi-inner divisors.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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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.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.907-916
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• 1995

The unilateral weighted shift operator $W_r$ with the weighted sequence ${r^n}^\infty_{n=0}$ is unicellular if $0 < r < 1$. In general, A + B is not unicellular even if A and B are unicellular. We will prove that $W_r + W^2_r$ is unicellular if $0 < r < 1$.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.723-737
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• 2010

In this paper, we investigate the sampling theorem for frame in multiwavelet subspaces. By the frame satisfying some special conditions, we obtain its dual frame with explicit expression. Then, we give an equivalent condition for the sampling theorem to hold in multiwavelet subspaces. Finally, a sufficient condition under which the sampling theorem holds is established. Some typical examples illustrate our results.

• Journal of KIISE:Computer Systems and Theory
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• v.33 no.3
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• pp.157-165
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• 2006

The change of external/internal factors of the cell rquires specific biological functions to maintain life. Such functions encourage particular genes to jnteract/regulate each other in multiple ways. Accordingly, we applied a linear decomposition model IFSA, which derives hidden variables, called the 'expression mode' that corresponds to the functions. To interpret gene interaction/regulation, we used a cross-correlation method given an expression mode. Linear decomposition models such as principal component analysis (PCA) and independent component analysis (ICA) were shown to be useful in analyzing high dimensional DNA microarray data, compared to clustering methods. These methods assume that gene expression is controlled by a linear combination of uncorrelated/indepdendent latent variables. However these methods have some difficulty in grouping similar patterns which are slightly time-delayed or asymmetric since only exactly matched Patterns are considered. In order to overcome this, we employ the (IFSA) method of [1] to locate phase- and shut-invariant features. Membership scoring functions play an important role to classify genes since linear decomposition models basically aim at data reduction not but at grouping data. We address a new function essential to the IFSA method. In this paper we stress that IFSA is useful in grouping functionally-related genes in the presence of time-shift and expression phase variance. Ultimately, we propose a new approach to investigate the multiple interaction information of genes.