• Title/Summary/Keyword: C-compact

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BOUNDED, COMPACT AND SCHATTEN CLASS WEIGHTED COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES

  • Wolf, Elke
    • Communications of the Korean Mathematical Society
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    • v.26 no.3
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    • pp.455-462
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    • 2011
  • An analytic self-map ${\phi}$ of the open unit disk $\mathbb{D}$ in the complex plane and an analytic map ${\psi}$ on $\mathbb{D}$ induce the so-called weighted composition operator $C_{{\phi},{\psi}}$: $H(\mathbb{D})\;{\rightarrow}\;H(\mathbb{D})$, $f{\mapsto} \;{\psi}\;(f\;o\;{\phi})$, where H($\mathbb{D}$) denotes the set of all analytic functions on $\mathbb{D}$. We study when such an operator acting between different weighted Bergman spaces is bounded, compact and Schatten class.

Electrodeposition of lead from $PbCl_2$-Acetate-Succinate Solutions (염화인-아세트산-숙신산 염 용액에서 납의 전해석출)

  • Kang, Tak
    • Journal of the Korean institute of surface engineering
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    • v.19 no.2
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    • pp.44-50
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    • 1986
  • Effects of cathodic overvoltages on the electrodeposition of lead from electrolyte containing lead chloride, ammonium acetate and sodium succinate was investigated at 20$^{\circ}C$. The use of organic additives, phenol and gelatin was found effective to inhibit the growth of dendritic crystals. At the carthodic overvoltages higher than 0.2V, the lead deposit becames less compact even in the presence of organic additives. The applications of agitation and pulse current promoted compact and shiny deposits.

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One-sided best simultaneous $L_1$-approximation for a compact set

  • Park, Sung-Ho;Rhee, Hyang-Joo
    • Bulletin of the Korean Mathematical Society
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    • v.35 no.1
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    • pp.127-140
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    • 1998
  • In this paper, we discuss the characterizations and uniqueness of a one-sided best simultaneous approximation for a compact subset from a convex subset of a finite-dimensional subspace of a normed linear space $C_1(X)$. The motivation is furnished by the characterizations of the one-sided best simultaneous approximations for a finite subset ${f_1, \ldots, f_\ell}$ for any $\ell \in N$.

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PRESERVATION OF EXPANSIVITY IN HYPERSPACE DYNAMICAL SYSTEMS

  • Koo, Namjip;Lee, Hyunhee
    • Journal of the Korean Mathematical Society
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    • v.58 no.6
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    • pp.1421-1431
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    • 2021
  • In this paper we study the preservation of various notions of expansivity in discrete dynamical systems and the induced map for n-fold symmetric products and hyperspaces. Then we give a characterization of a compact metric space admitting hyper N-expansive homeomorphisms via the topological dimension. More precisely, we show that C0-generically, any homeomorphism on a compact manifold is not hyper N-expansive for any N ∈ ℕ. Also we give some examples to illustrate our results.

ON THE DENSITY OF VARIOUS SHADOWING PROPERTIES

  • Koo, Namjip;Tsegmid, Nyamdavaa
    • Communications of the Korean Mathematical Society
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    • v.34 no.3
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    • pp.981-989
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    • 2019
  • In this paper we deal with some shadowing properties of discrete dynamical systems on a compact metric space via the density of subdynamical systems. Let $f:X{\rightarrow}X$ be a continuous map of a compact metric space X and A be an f-invariant dense subspace of X. We show that if $f{\mid}_A:A{\rightarrow}A$ has the periodic shadowing property, then f has the periodic shadowing property. Also, we show that f has the finite average shadowing property if and only if $f{\mid}_A$ has the finite average shadowing property.