• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.773-786
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• 2001

On the setting of the half-space of the Euclidean n-space, we consider harmonic Bergman spaces and we also study properties of the reproducing kernel. Using covering lemma, we find some equivalent quantities. We prove that if lim$ lim\limits_{i\rightarrow\infty}\frac{\mu(K_r(zi))}{V(K_r(Z_i))}$ then the inclusion function $I : b^p\rightarrow L^p(H_n, d\mu)$ is a compact operator. Moreover, we show that if f is a nonnegative continuous function in $L^\infty and lim\limits_{Z\rightarrow\infty}f(z) = 0, then T_f$ is compact if and only if f $\in$ $C_{o}$ (H$_{n}$ ).

• Communications for Statistical Applications and Methods
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• v.21 no.4
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• pp.317-325
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• 2014

Consider a nonlinear transform ${\Phi}(x)$ of x in $\mathbb{R}^p$ to Hilbert space H and assume that the dot product between ${\Phi}(x)$ and ${\Phi}(x^{\prime})$ in H is given by < ${\Phi}(x)$, ${\Phi}(x^{\prime})$ >= K(x, x'). The aim of this paper is to propose a mathematical technique to take screen shots of the multivariate dataset mapped to Hilbert space H, particularly suited to Gaussian kernel $K({\cdot},{\cdot})$, which is defined by $K(x,x^{\prime})={\exp}(-{\sigma}{\parallel}x-x^{\prime}{\parallel}^2)$, ${\sigma}$ > 0. Several numerical examples are given.

• Korean Journal of Crystallography
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• v.12 no.3
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• pp.141-144
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• 2001

From the reaction of Na[Ga(N₃)₄] with PPh₃, an ionic compound [Ph₃P(OH)]/sup +/[N₃]/sup -/ (1) was isolated. Compound 1 was characterized by spectroscopy (¹H-NMR, /sup 13C{¹H}-NMR, and IR) and X-ray diffraction. Crystallographic data for 1 : orthorhombic space group P2₁2₁2₁, a = 10.491 (4) Å, b=11.603(5)Å, c=13.149(5)Å, Z=4, R(wR₂)=0.0547(0.0978).

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.375-415
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• 2019

We study spaces of continuous-function-valued functions that have the property that composition with evaluation functionals induce $weak^*$ to norm continuous maps to ${\ell}^p$ space ($p{\in}(1,\;{\infty})$). Versions of $H{\ddot{o}}lder^{\prime}s$ inequality and Riesz representation theorem are proved to hold on these spaces. We prove a version of Dixmier's theorem for spaces of function-valued matrix operators on these spaces, and an analogue of the trace formula for operators on Hilbert spaces. When the function space is taken to be the complex field, the spaces are just the ${\ell}^p$ spaces and the well-known classical theorems follow from our results.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.251-264
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• 1995

Applications of the classical Knaster-Kuratowski-Mazurkiewicz (si-mply, KKM) theorem and the fixed point theory of multifunctions defined on convex subsets of topological vector spaces have been greatly improved by adopting the concept of convex spaces due to Lassonde [L1]. In this direction, the first author [P5] found that certain coincidence theorems on a large class of composites of upper semicontinuous multifunctions imply many fundamental results in the KKM theory.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.469-479
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• 2003

Let B be the open unit ball in $C^{n}$ and ${\mu}_{q}$(q > -1) the Lebesgue measure such that ${\mu}_{q}$(B) ＝ 1. Let ${L_{a,q}}^2$ be the subspace of ${L^2(B,D{\mu}_q)$ consisting of analytic functions, and let $\overline{{L_{a,q}}^2}$ be the subspace of ${L^2(B,D{\mu}_q)$) consisting of conjugate analytic functions. Let $\bar{P}$ be the orthogonal projection from ${L^2(B,D{\mu}_q)$ into $\overline{{L_{a,q}}^2}$. The little Hankel operator ${h_{\varphi}}^{q}\;:\;{L_{a,q}}^2\;{\rightarrow}\;{\overline}{{L_{a,q}}^2}$ is defined by ${h_{\varphi}}^{q}(\cdot)\;=\;{\bar{P}}({\varphi}{\cdot})$. In this paper, we will find the necessary and sufficient condition that the little Hankel operator ${h_{\varphi}}^{q}$ is bounded(or compact).

• The Pure and Applied Mathematics
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• v.11 no.4
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• pp.287-292
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• 2004

The operator $A \; {\in} \; L(H_{i})$, the Banach algebra of bounded linear operators on the complex infinite dimensional Hilbert space $\cal H_{i}$, is said to be p-hyponormal if $(A^\ast A)^P \geq (AA^\ast)^p$ for $p\; \in \; (0,1]$. Let (equation omitted) denote the completion of (equation omitted) with respect to some crossnorm. Let $I_{i}$ be the identity operator on $H_{i}$. Letting (equation omitted), where each $A_{i}$ is p-hyponormal, it is proved that the commuting n-tuple T = ($T_1$,..., $T_{n}$) satisfies Bishop's condition ($\beta$) and that if T is Weyl then there exists a non-singular commuting n-tuple S such that T = S + F for some n-tuple F of compact operators.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.889-895
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• 1995

Let $H$ be a separable, infinite dimensional, complex Hilbert space and let $L(H)$ denote the algebra of all bounded linear operators on $H$.

• The Bulletin of The Korean Astronomical Society
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• v.35 no.2
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• pp.27.2-27.2
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• 2010

We report the HST pixel analysis results of the interacting face-on spiral galaxy, NGC 5194 (M51), which is the first step of a new observational research project, PANCluG (Pixel Analysis of Nearby Cluster Galaxies). We derive several quantities describing the pixel color-magnitude diagram (pCMD) of NGC 5194, suitable for future comparisons with the pCMDs of other galaxies. We investigate the spatial distribution of pixel stellar populations, finding that the spiral arm pattern and the tidal interaction with NGC 5195 significantly affect the stellar populations in NGC 5194. We find that the pixels corresponding to the central active galactic nucleus (AGN) of NGC 5194 show a very tight sequence in the bright-end of the pCMD, of which spatial distribution seems to agree with the AGN torus region.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.489-509
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• 2024

In this paper, let q ∈ (0, 1]. We establish the boundedness of intrinsic g-functions from the Hardy-Lorentz spaces with variable exponent H^p(·),q(ℝⁿ) into Lorentz spaces with variable exponent L^p(·),q(ℝⁿ). Then, for any q ∈ (0, 1], via some estimates on a discrete Littlewood-Paley g-function and a Peetre-type maximal function, we obtain several equivalent characterizations of H^p(·),q(ℝⁿ) in terms of wavelets.