• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.973-986
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• 2020

In this paper, we compute the Hankel matrix representation of the Hankel operator on the Hardy space of a general bounded domain with respect to special orthonormal bases for the Hardy space and its orthogonal complement. Moreover we obtain the compact form of the Hankel matrix for the unit disc case with respect to these bases. One can see that the Hankel matrix generated by this computation turns out to be a generalization of the case of the unit disc from the single simply connected domain to multiply connected domains with much diversities of bases.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.641-651
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• 2011

In this paper, with use of the displacement matrix, two special matrices are constructed. By these special matrices the block decompositions of the block symmetric Hankel matrix and the inverse of the Hankel matrix are derived. Hence, the algorithms according to these decompositions are given. Furthermore, the numerical tests show that the algorithms are feasible.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.821-835
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• 2023

Hankel operators and their variants have abundant applications in numerous fields. For a non-zero complex number r, the r-Hankel operators on a Hilbert space 𝓗 define a class of one such variant. This article introduces and explores some properties of two other variants of Hankel operators namely k^th-order (C, r)-Hankel operators and k^th-order (R, r)-Hankel operators (k ≥ 2) which are closely related to r-Hankel operators in such a way that a k^th-order (C, r)-Hankel matrix is formed from r^k-Hankel matrix on deleting every consecutive (k - 1) columns after the first column and a k^th-order (R, r^k)-Hankel matrix is formed from r-Hankel matrix if after the first column, every consecutive (k - 1) columns are deleted. For |r| ≠ 1, the characterizations for the boundedness of these operators are also completely investigated. Finally, an appropriate approach is also presented to extend these matrices to two-way infinite matrices.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.187-200
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• 2019

Truncated Hankel operators are compressions of classical Hankel operators to model spaces. In this paper we describe matrix representations of truncated Hankel operators on finite-dimensional model spaces. We then show that the obtained descriptions hold also for some infinite-dimensional cases.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.418-432
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• 2023

In this study, we consider the Hankel and Gram matrices which are defined by the elements of special number sequences. Firstly, the eigenvalues, determinant, and norms of the Hankel matrix defined by special number sequences are obtained. Afterwards, using the relationship between the Gram and Hankel matrices, the eigenvalues, determinants, and norms of the Gram matrices defined by number sequences are given.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.691-700
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• 2021

In this paper, we compute directly the Hankel matrix representation of the Hankel operator on the Hardy space of the unit disc without using any classical kernel functions with respect to special orthonormal bases for the Hardy space and its orthogonal complement. This gives an elementary proof for the formula.

• Journal of the Korea institute for structural maintenance and inspection
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• v.20 no.4
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• pp.27-34
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• 2016

A new algorithm for determining optimal accelerometer locations is proposed by using a frequency-domain Hankel matrix which is much simpler to construct than a time-domain Hankel matrix. The algorithm was examined through simulation studies by comparing the outcomes with those from other available methods. To compare and analyze the results from different methods, a dynamic analysis was carried out under seismic excitation and acceleration data were obtained at the selected optimal sensor locations. Vibrational amplitudes at the selected sensor locations were determined and those of all the other degrees of freedom were determined by using a spline function. MAC index of each method was calculated and compared to look at which method could determine more effective locations of accelerometers. The proposed frequency-domain Hankel matrix could determine reasonable selection of accelerometer locations compared with the others.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.2
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• pp.99-112
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• 2013

This paper presents a subspace system identification for estimating the stiffness matrix and flexural rigidities of a shear building. System matrices are estimated by LQ decomposition and singular value decomposition from an input-output Hankel matrix. The estimated system matrices are converted into a real coordinate through similarity transformation, and the stiffness matrix is estimated from the system matrices. The accuracy and the stability of an estimated stiffness matrix depend on the size of the associated Hankel matrix. The estimation error curve of the stiffness matrix is obtained with respect to the size of a Hankel matrix using a prior finite element model of a shear building. The sizes of the Hankel matrix, which are consistent with a target accuracy level, are chosen through this curve. Among these candidate sizes of the Hankel matrix, more proper one can be determined considering the computational cost of subspace identification. The stiffness matrix and flexural rigidities are estimated using the Hankel matrix with the candidate sizes. The validity of the proposed method is demonstrated through the numerical example of a five-story shear building model with and without damage.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.703-721
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• 2019

The notion of slant H-Toeplitz operator $V_{\phi}$ on the Hardy space $H^2$ is introduced and its characterizations are obtained. It has been shown that an operator on the space $H^2$ is a slant H-Toeplitz if and only if its matrix is a slant H-Toeplitz matrix. In addition, the conditions under which slant Toeplitz and slant Hankel operators become slant H-Toeplitz operators are also obtained.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1452-1455
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• 1997

This paper studies the problem of approximating commensurate input delay sustems by finite dimensional systems based on the Hankel singular values. I is shown that the Gankel singular values are solutions a trancendental equation and the Hankel singular vectors are obtained form the kernel of the matrix. The computaioin is carried out in state spae framework. Once singular values and vectors are calcualted, finite dimensional approximated systems are constructed using stadnard linear system computational tools. An example is included.