• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.561-569
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• 1997

In this paper we shall characterize a finite triangular operator matrix with M-hyponormal operators on main diagonal. This shows in particualr that such an operator is subscalar operator. As a corollary, we get that every algebraic operator is subscalar.

• Structural Engineering and Mechanics
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• v.35 no.2
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• pp.175-190
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• 2010

One of the intractable problems in multiresolution structural analysis is the decoupling computation between scales, which can be realized by the operator-orthogonal wavelets based on the lifting scheme. The multiresolution finite element space is described and the formulation of multiresolution finite element models for structural problems is discussed. Various operator-orthogonal wavelets are constructed by the lifting scheme according to the operators of multiresolution finite element models. A dynamic multiresolution algorithm using operator-orthogonal wavelets is proposed to solve structural problems. Numerical examples demonstrate that the lifting scheme is a flexible and efficient tool to construct operator-orthogonal wavelets for multiresolution structural analysis with high convergence rate.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.63-71
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• 2015

Let H be a separable infinite dimensional complex Hilbert space, and let $\mathcal{L}(H)$ denote the algebra of all bounded linear operators on H into itself. Let $A,B{\in}\mathcal{L}(H)$ we define the generalized derivation ${\delta}_{A,B}:\mathcal{L}(H){\mapsto}\mathcal{L}(H)$ by ${\delta}_{A,B}(X)=AX-XB$, we note ${\delta}_{A,A}={\delta}_A$. If the inequality ${\parallel}T-(AX-XA){\parallel}{\geq}{\parallel}T{\parallel}$ holds for all $X{\in}\mathcal{L}(H)$ and for all $T{\in}ker{\delta}_A$, then we say that the range of ${\delta}_A$ is orthogonal to the kernel of ${\delta}_A$ in the sense of Birkhoff. The operator $A{\in}\mathcal{L}(H)$ is said to be finite [22] if ${\parallel}I-(AX-XA){\parallel}{\geq}1(*)$ for all $X{\in}\mathcal{L}(H)$, where I is the identity operator. The well-known inequality (*), due to J. P. Williams [22] is the starting point of the topic of commutator approximation (a topic which has its roots in quantum theory [23]). In [16], the author showed that a paranormal operator is finite. In this paper we present some new classes of finite operators containing the class of paranormal operators and we prove that the range of a generalized derivation is orthogonal to its kernel for a large class of operators containing the class of normal operators.

• East Asian mathematical journal
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• v.16 no.1
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• pp.97-103
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• 2000

In this work, we consider a finite difference operator $L^2_N$ corresponding to $$Lu:=-(u_{xx}+u_{yy})\;in\;{\Omega},\;u=0\;on\;{\partial}{\Omega}$$, in $S_{h^2,1}$. We derive the relation between the absolute value of the bilinear form $l_{N^2}$(u, v) on $S_{h^2,1}{\times}S_{h^2,1}$ and Sobolev $H^1$ norms.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.609-614
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• 2010

We prove that if graphs of bounded degree are roughly isometric to each other, then the spaces of bounded energy finite solutions of the Schr$\ddot{o}$dinger operator on the graphs are isomorphic to each other. This is a direct generalization of the results of Soardi [5] and of Lee [3].

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.885-892
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• 2015

In this paper, we mainly obtain the following assertions: (1) If T is a quasi-*-n-paranormal operator, then T is finite and simply polaroid. (2) If T or $T^*$ is a quasi-*-n-paranormal operator, then Weyl's theorem holds for f(T), where f is an analytic function on ${\sigma}(T)$ and is not constant on each connected component of the open set U containing ${\sigma}(T)$. (3) If E is the Riesz idempotent for a nonzero isolated point ${\lambda}$ of the spectrum of a quasi-*-n-paranormal operator, then E is self-adjoint and $EH=N(T-{\lambda})=N(T-{\lambda})^*$.

• Korean Journal of Mathematics
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• v.32 no.1
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• pp.1-14
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• 2024

We seek for an invertible map B from L²(Γ) to L²(G), where G is a finite abelian group and Γ is the direct product of finite cyclic groups which is isomorphic to G, so that any Gabor frame in L²(G), is a generalized pseudo B-Gabor frame.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.321-334
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• 2022

We introduce a special class of structured frames having single generators in finite dimensional Hilbert spaces. We call them as pseudo B-Gabor like frames and present a characterisation of the frame operators associated with these frames. The concept of Gabor semi-frames is also introduced and some significant properties of the associated semi-frame operators are discussed.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.61-82
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• 2000

In this paper two so-called regularized Green's functions are introduced to derive the optimal maximum norm error estimates for the unknown function and the adjoint vector-valued function for mixed finite element methods of Laplacian operator. One contribution of the paper is a demonstration of how the boundedness of $L^1$-norm estimate for the second Green's function ${\lambda}_2$ and the optimal maximum norm error estimate for the adjoint vector-valued function are proved. These results are seemed to be to be new in the literature of the mixed finite element methods.

• Transactions on Control, Automation and Systems Engineering
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• v.3 no.4
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• pp.242-249
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• 2001

In this paper, the open-loop state response of the two-time-scale systems by unified approach using the $\delta$-operator is presented with an example of the aircraft longitudinal dynamics. First, the $\delta$-operator system unifies both the continuous system and the discrete system simultaneously, and the $\delta$-operator approach improves the finite word-length characteristics. This saves more computing time than that of the discrete system. Second, the singular perturbation method by block diagonalization reduces the sizes and orders of the systems. This also reduces the floating-point operations (flops). The advantage of those two approaches is shown by comparing our results with the earlier ones in the illustrative example of the longitudinal motion of F-8 aircraft.