• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.537-545
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• 2012

In the present paper, we show that a continuous linear operator T on a Frechet space satisfies the Hypercyclic Criterion with respect to a syndetic sequence must satisfy the Kitai Criterion. On the other hand, an operator, hereditarily hypercyclic with respect to a syndetic sequence must be mixing. We also construct weighted shift operators satisfying the Hypercyclicity Criterion which do not satisfy the Kitai Criterion. In other words, hereditarily hypercyclic operators without being mixing.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.903-924
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• 2016

In the present paper, using a simple formula for the conditional expectations given a generalized conditioning function over an analogue of vector-valued Wiener space, we prove that the analytic operator-valued Feynman integrals of certain classes of functions over the space can be expressed by the conditional analytic Feynman integrals of the functions. We then provide the conditional analytic Feynman integrals of several functions which are the kernels of the analytic operator-valued Feynman integrals.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.685-692
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• 2003

In this paper, we study some properties of (equation omitted) (defined below). In particular we show that an operator T $\in$(equation omitted) satisfying the translation invariant property is hyponormal and an invertible operator T $\in$ (equation omitted) and its inverse T$^{-1}$ have a common nontrivial invariant closed set. Also we study some cases which have nontrivial invariant subspaces for an operator in (equation omitted).

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.309-313
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• 2007

By applying ideas from [M. S. Moslehian, et al., Norms of operators in $X_{\lambda}$ spaces, Appl. Math. Lett. (2007), doi:10.1016/j.aml.2006. 11.009], we investigate the norm of the cubic operator on the function space $X_{\lambda}$.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.787-798
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• 2018

For $1{\leq}p{\leq}{\infty}$, let $H^p$ be the usual Hardy space on the unit circle. When ${\alpha}$ and ${\beta}$ are bounded functions, a singular integral operator $S_{{\alpha},{\beta}}$ is defined as the following: $S_{{\alpha},{\beta}}(f+{\bar{g}})={\alpha}f+{\beta}{\bar{g}}(f{\in}H^p,\;g{\in}zH^p)$. When p = 2, we study the hyponormality of $S_{{\alpha},{\beta}}$ when ${\alpha}$ and ${\beta}$ are some special functions.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.207-213
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• 2003

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx=y. An interpolating operator for n-vectors satisfies the equation Ax$_{i}$=y$_{i}$. for i=1,2, …, n. In this article, we investigate unitary interpolation problems in CSL-Algebra AlgL : Let L be a commutative subspace lattice on a Hilbert space H. Let x and y be vectors in H. When does there exist a unitary operator A in AlgL such that Ax=y?

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.337-345
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• 2004

In allelic model X = ($\chi_1\chi$_2ㆍㆍㆍ, \chi_d$), M_f(t) = f(p(t)) - ${{\int^t}_0}\;Lf(p(t))ds$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we can show existence and uniqueness of solution for stochastic differential equation and martingale problem associated with mean vector. Also, we examine that if the operator related to this martingale problem is connected with Markov processes under certain circumstance, then this operator must satisfy the maximum principle.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.233-246
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• 2016

In this paper, we introduce the class of analytic extensions of M-hyponormal operators and we study various properties of this class. We also use a special Sobolev space to show that every analytic extension of an M-hyponormal operator T is subscalar of order 2k + 2. Finally we obtain that an analytic extension of an M-hyponormal operator satisfies Weyl's theorem.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.147-159
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• 2016

In this paper, subordination results of analytic function $f{\in}{\mathcal{A}}_p$ involving linear operator ${\mathcal{K}}^{{\delta},{\lambda}}_{c,p}$ are obtained. By applying the differential subordination method, results are derived under some sufficient subordination conditions. On using some hypergeometric identities, corollaries of the main results are derived. Furthermore, convolution preserving properties for a class of multivalent analytic function associated with the operator ${\mathcal{K}}^{{\delta},{\lambda}}_{c,p}$ are investigated.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.1031-1051
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• 2015

The object of the present paper is to derive some inclusion and subordination results for certain classes of multivalent analytic functions in the open unit disk, which are defined in terms of the Cho-Kwon-Srivastava operator. Some interesting corollaries are derived and the relevant connection of the results obtained in this paper with various known results are also pointed out.