• Honam Mathematical Journal
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• v.29 no.1
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• pp.1-8
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• 2007

In this paper we show that for each finite frame for a Hilbert space there are two orthonormal elements related to the optimal lower and upper bounds of the frame. Based on this we show that an orthonormal basis is naturally associated with every finite frame. We then analyze the relationship between such an orthonormal basis and the given finite frame.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2013-2027
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• 2017

We compute explicitly the matrices represented by Toeplitz operators on the Hardy space over the unit circle with respect to a special orthonormal basis constructed by author in terms of their symbols. And we also find a necessary condition for the matrix generated by the product of two Toeplitz operators with respect to the basis to be a Toeplitz matrix by a direct calculation and we finally solve commuting problems of two Toeplitz operators in terms of symbols. This is a generalization of the classical results obtained regarding to the orthonormal basis consisting of the monomials.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.777-786
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• 2014

We construct an orthonormal basis for the Bergman space associated to a simply connected domain. We use the or-thonormal basis for the Hardy space consisting of the Szegő kernel and the Riemann mapping function and rewrite their area integrals in terms of arc length integrals using the complex Green's identity. And we make a note about the matrix of a Toeplitz operator with respect to the orthonormal basis constructed in the paper.

• Kyungpook Mathematical Journal
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• v.53 no.1
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• pp.135-141
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• 2013

In this paper we show that a $g$-frame for a Hilbert space $\mathcal{H}$ can be written as a linear combination of two $g$-orthonormal bases for $\mathcal{H}$ if and only if it is a $g$-Riesz basis for $\mathcal{H}$. Also, we show that every $g$-frame for a Hilbert space $\mathcal{H}$ is a multiple of a sum of three $g$-orthonormal bases for $\mathcal{H}$.

• Honam Mathematical Journal
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• v.37 no.3
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• pp.335-337
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• 2015

We modify the normalizing constants of the functions in the orthonormal basis for the Bergman space and restate their consequences in the paper that was published in Honam Math. J. 36 (2014), no. 4, pp. 777-786.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.1
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• pp.45-60
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• 1995

It is attempted to estimate excitation force of a linear vibratory system using measured vibration responses. The excitation force is estimated from the relationship between the vibration response and system characteristic matrices which are extracted from both the mathematical model of the system and actual response in contrast to the usual approach of inverting the frequency response matrices. This extraction scheme is based on the fact that the vibration response can be expressed in term of linear combination of frequency domain modal vectors defined as mutually orthonormal basis vectors in frequency domain. The extracted frequency domain basis vectors are very stable in computational manipulation. It is found that the estimated excitation force is in good agreement with actually measured force except at the natural frequencies the structure, which is the common feature still to be overcome by the research efforts in this area. From the results of this paper, this disagreement is considered to come from the discrepancy between the model and actual value of the mass, damping and stiffness of the structure.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1996.06a
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• pp.233-236
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• 1996

A new method of blocking effects reduction is proposed in this paper for use in low bitrate image coding. We use 28 DCT kernel functions of which boundary values are linearly independent, and Gram-Schmidt process is applied to the boundary values in order to obtain 28 boundary-orthonormal basis images. Then we use these basis images to obtain the correction terms for blocking artifacts reduction. A threshold of block discontinuity is introduced for improvement of visual quality by reducing image blurring. We also investigate the number of basis images needed for efficient blocking artifacts reduction when the compression ratio changes.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1135-1143
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• 2019

The matrix representation of the Toeplitz operator on the Hardy space with respect to a generalized orthonormal basis for the space of square integrable functions associated to a bounded simply connected region in the complex plane is completely computed in terms of only the Szegő kernel and the Garabedian kernels.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1119-1129
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• 2022

We formulate the matrix representation of a composition operator on the Hardy space of the unit disc with the symbol which is a Riemann map of the unit disc, with respect to a special orthonormal basis.

• Honam Mathematical Journal
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• v.46 no.1
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• pp.60-69
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• 2024

We consider a special orthonormal basis for the Hardy space of the unit disc to compute the matrix representations of the composition operators with respect to the basis particulary associated to two symbols which are the inverse and the origin symmetry of the Riemann self map in the unit disc, and then we find a certain symmetry of the matrices.