• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.263-279
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• 2009

On the setting of the unit ball of ${\mathbb{R}}^n$, we consider a Banach space of harmonic functions motivated by the atomic decomposition in the sense of Coifman and Rochberg [5]. First we identify its dual (resp. predual) space with certain harmonic function space of (resp. vanishing) logarithmic growth. Then we describe these spaces in terms of boundedness and compactness of certain Toeplitz operators.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1221-1228
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• 2017

We consider weighted Hardy spaces on bidisk ${\mathbb{D}}^2$ which generalize the weighted Bergman spaces $A^2_{\alpha}({\mathbb{D}}^2)$. Let z, w be coordinate functions and $T_{{\bar{z}}^N}_w$ Toeplitz operator with symbol $_{{\bar{z}}^N}_w$. In this paper, we study the reducing subspaces of $T_{{\bar{z}}^N}_w$ on the weighted Hardy spaces.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.127-135
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• 2008

In this paper we consider the hyponormality of Toeplitz operators $T_{\varphi}$ on the Bergman space $L^2_a(\mathbb{D})$ with symbol in the case of function f + $\overline{g}$ with polynomials f and g. We present some necessary conditions for the hyponormality of $T_{\varphi}$, under certain assumptions about the coefficients of ${\varphi}$.

• Journal of Communications and Networks
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• v.7 no.3
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• pp.278-283
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• 2005

This paper proposes a blind channel estimation scheme for long code direct sequence code division multiple access (DS­CDMA) systems with multipath fading channels. This scheme combines the advantages of Toeplitz displacement and correlation matching methods to achieve improved performance. The basic idea is to remove the effects of noise and interferences with Toeplitz displacement operation and then estimate the multi path channel parameters with the correlation matching method. Simulation results are presented to show that the proposed scheme provides better MSE performance and robustness against the near-far problem.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.585-590
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• 2016

Suppose $T_{\varphi}$ is a 2-hyponormal Toeplitz operator whose self-commutator has rank $n{\geq}1$. If $H_{\bar{\varphi}}(ker[T^*_{\varphi},T_{\varphi}])$ contains a vector $e_n$ in a canonical orthonormal basis $\{e_k\}_{k{\in}Z_+}$ of $H^2({\mathbb{T}})$, then ${\varphi}$ should be an analytic function of the form ${\varphi}=qh$, where q is a finite Blaschke product of degree at most n and h is an outer function.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1185-1192
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• 2020

In this paper, we introduce and investigate multi subspace-hypercyclic operators and prove that multi-hypercyclic operators are multi subspace-hypercyclic. We show that if T is M-hypercyclic or multi M-hypercyclic, then Tⁿ is multi M-hypercyclic for any natural number n and by using this result, make some examples of multi subspace-hypercyclic operators. We prove that multi M-hypercyclic operators have somewhere dense orbits in M. We show that analytic Toeplitz operators can not be multi subspace-hypercyclic. Also, we state a sufficient condition for coanalytic Toeplitz operators to be multi subspace-hypercyclic.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.633-637
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• 2009

We prove using the Szeg$\H{o}$ kernel and the Garabedian kernel that a Toeplitz operator on the boundary of $C^{\infty}$ smoothly bounded domain associated to a smooth symbol vanishes only when the symbol vanishes identically. This gives a generalization of previous results on the unit disk to more general domains in the plane.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.311-317
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• 2013

In this note we consider the hyponormality of Toeplitz operators $T_{\varphi}$ on the Weighted Bergman space $A^2_{\alpha}(\mathbb{D})$ with symbol in the class of functions $f+\bar{g}$ with polynomials $f$ and $g$ of degree 2.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.465-481
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• 2021

Let f be the function defined on the open unit disk, with f(0) = 0 = f'(0) - 1, satisfying Re (αf'(z) + (1 - α)zf'(z)/f(z)) > 0 or Re (αf'(z) + (1 - α)(1 + zf"(z)/f'(z)) > 0 respectively, where 0 ≤ α ≤ 1. Estimates for the Toeplitz determinants have been obtained when the elements are the coefficients of the functions belonging to these two subclasses.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1041-1053
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• 2022

In this paper, sharp lower and upper bounds on the third order Hermitian-Toeplitz determinant for the classes of Sakaguchi functions and some of its subclasses related to right-half of lemniscate of Bernoulli, reverse lemniscate of Bernoulli and exponential functions are investigated.