• 대한수학회지
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• 제54권2호
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• pp.627-645
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• 2017

In this paper, we characterize the boundedness, compactness and essential norm of products of differentiation and composition operators from the Bloch space and weighted Dirichlet spaces to analytic Morrey type spaces.

• 대한수학회보
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• 제51권4호
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• pp.1187-1193
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• 2014

We will characterize the boundedness and compactness of weighted composition operators on the minimal M$\ddot{o}$bius invariant space.

• 대한수학회보
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• 제51권4호
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• pp.1005-1013
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• 2014

Let ${\phi}$ be an analytic self map of the open unit disc D. In this paper, we study the composition operator $C_{\phi}$ from the Bergman space on D to the Hardy space on D.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.125-130
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• 2016

A finite rank difference of two composition operators is studied on a Hilbert Lebesgue space or a Hilbert Hardy space.

• Kyungpook Mathematical Journal
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• 제50권1호
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• pp.89-100
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• 2010

Let g = (V, E, ${\mu}$) be a weighted directed tree, where V is a vertex set, E is an edge set, and ${\mu}$ is ${\sigma}$-finite measure on V. The tree g induces a composition operator C on the Hilbert space $l^2$(V). Hand-type directed trees are defined and characterized the weak hyponormalities of such C in this note. Also some additional related properties are discussed. In addition, some examples related to directed hand-type trees are provided to separate classes of weak-hyponormal operators.

• 대한수학회보
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• 제54권1호
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• pp.187-198
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• 2017

We obtain some necessary and sufficient conditions for the boundedness of the composition operators between weighted Bergman spaces of logarithmic weights. In terms of the conditions for the boundedness, we compute the essential norm of the composition operators.

• 대한수학회논문집
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• 제30권3호
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• pp.169-176
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• 2015

A sequence of composition operators on Hardy space is considered. We prove that, by numerical range properties, it is SOT-convergence but not converge.

• 대한수학회보
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• 제41권3호
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• pp.413-418
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• 2004

Invertible and isometric composition operators acting on vector-valued Hardy space $H^2$(E) are characterized.

• 대한수학회지
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• 제54권4호
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• pp.1063-1079
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• 2017

Two standard Bessel sequences in a Hilbert $C^*$-module are approximately duals if the distance (with respect to the norm) between the identity operator on the Hilbert $C^*$-module and the operator constructed by the composition of the synthesis and analysis operators of these Bessel sequences is strictly less than one. In this paper, we introduce (a, m)-approximate duality using the distance between the identity operator and the operator defined by multiplying the Bessel multiplier with symbol m by an element a in the center of the $C^*$-algebra. We show that approximate duals are special cases of (a, m)-approximate duals and we generalize some of the important results obtained for approximate duals to (a, m)-approximate duals. Especially we study perturbations of (a, m)-approximate duals and (a, m)-approximate duals of modular Riesz bases.

• 대한수학회논문집
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• 제17권2호
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• pp.349-361
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• 2002

The ill-posed elliptic wave propagation problems can be transformed into well-posed initial value problems of the reflection and transmission operators characterizing the material structure of the given model by the combination of wave field splitting and invariant imbedding methods. In general, the derived scattering operator equations are of first-order in range, nonlinear, nonlocal, and stiff and oscillatory with a subtle fixed and movable singularity structure. The phase space and path integral analysis reveals that construction and reconstruction algorithms depend crucially on a detailed symbol analysis of the scattering operators. Some information about the singularity structure of the scattering operator symbols is presented and analyzed in the transversely homogeneous limit.