• Journal of the Korean Mathematical Society
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• v.59 no.5
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• pp.987-996
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• 2022

We introduce the notions of symbolic expansivity and symbolic shadowing for homeomorphisms on non-metrizable compact spaces which are generalizations of expansivity and shadowing, respectively, for metric spaces. The main result is to generalize the Smale's spectral decomposition theorem to symbolically expansive homeomorphisms with symbolic shadowing on non-metrizable compact Hausdorff totally disconnected spaces.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.504-512
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• 1994

A simple proof for the random central limit theorem is given for a family of stationary linear lattice processes, which belogn to a class of 2 dimensional random fields, applying the Beveridge and Nelson decomposition in time series context. The result is an extension of Fakhre-Zakeri and Fershidi (1993) dealing with the linear process in time series to the case of the linear lattice process with 2 dimensional indices.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.403-416
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• 2015

An operator T on a complex Hilbert space $\mathcal{H}$ is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for $\mathcal{H}$. In this note, we explore the structure of skew symmetric operators with disconnected spectra. Using the classical Riesz decomposition theorem, we give a decomposition of certain skew symmetric operators with disconnected spectra. Several corollaries and illustrating examples are provided.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1183-1193
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• 2011

In this paper, we introduce a notion of Lie operator algebras which as a generalization of ordinary Lie algebras is an analogy of operator groups. We discuss some elementary properties of Lie operator algebras. Moreover, we also prove a decomposition theorem for Lie operator algebras.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.91-101
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• 2022

We study some properties of nonwandering set Ω(𝜙) and chain recurrent set CR(𝜙) for an expansive flow which has the POTP on a compact TVS-cone metric spaces. Moreover we shall prove a spectral decomposition theorem for an expansive flow which has the POTP on TVS-cone metric spaces.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.503-503
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• 1994

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.561-575
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• 2001

Making use of the singular spectrum in the Denjoy-Carleman class we prove the microlocal decomposition theorem and quasianalytic versions of Holmgren's uniqueness theorem and watermelon theorem.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.959-965
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• 1996

In this paper we study the index stability theorem for a bounded linear operator with closed range and extend the Kato's decomposition theorem for an absence of the index.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.347-351
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• 1993

The dichotomy of absolute continuity and singularity for a pair of stationary and ergodic measures (one of which need not be ergodic) is obtained using the ergodic decomposition theorem. The known fact that two different stationary and ergodic measures are mutually singular is obtained as a corollary of our result. An example of a pair of stationary-ergodic measures enjoying the dichotomy is presented.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.337-344
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• 2018

We extend Bowen's decomposition theorem to topologically Anosov homeomorphisms on first countable, locally compact, paracompact, Hausdorff spaces which are not necessarily metrizable and not necessarily compact.