• 정보학연구
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• 제5권1호
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• pp.133-142
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• 2002

본 논문에서는 linear window operator의 효율적인 구현 방안을 제안하였다. 블록 상태 공간함수를 이용하여 computational primitive를 찾아내고 이를 이용하여 프로세사의 datapath의 구현에 사용함으로서 효율적인 linear window operator의 구현을 가능하게 하였다. 또한 linear window operator의 실시간 처리를 위하여 데이터 분할 기법을 사용한 다중 프로세서 구조를 제안하였다. 블록의 크기에 따른 성능 분석을 통하여 제시된 프로세서 및 다중 프로세서의 성능이 우수함을 보였다.

• 대한수학회지
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• 제53권2호
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• pp.347-362
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• 2016

In this paper, we are concerned with abstract random linear operators on probabilistic unitary spaces which are a generalization of generalized random linear operators on a Hilbert space defined in [25]. The representation theorem for abstract random bounded linear operators and some results on the adjoint of abstract random linear operators are given.

• 대한수학회논문집
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• 제23권4호
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• pp.541-548
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• 2008

For a completely bounded linear maps between operator spaces, we introduce numbers which measure the degree of injectivity and subjectivity. The number measuring the injectivity is an operator space analogue of the minimum modulus of a linear map in normed spaces.

• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.903-917
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• 2023

This paper constructs a new linear operator associated with a seven parameters Mittag-Leffler function using the convolution technique. In addition, it investigates some significant second-order differential subordination properties with considerable sandwich results concerning that operator.

• Kyungpook Mathematical Journal
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• 제46권1호
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• pp.89-96
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• 2006

For a rank-1 matrix A, there is a factorization as $A=ab^t$, the product of two vectors a and b. We characterize the linear operators that preserve rank and some equivalent condition of rank-1 matrices over a chain semiring. We also obtain a linear operator T preserves the rank of rank-1 matrices if and only if it is a form (P, Q, B)-operator with appropriate permutation matrices P and Q, and a matrix B with all nonzero entries.

• 충청수학회지
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• 제16권1호
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• pp.37-48
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• 2003

In this paper, we show that for a pure hyponormal operator the analytic spectral subspace and the algebraic spectral subspace are coincide. Using this result, we have the following result: Let T be a decomposable operator on a Banach space X and let S be a pure hyponormal operator on a Hilbert space H. Then every linear operator ${\theta}:X{\rightarrow}H$ with $S{\theta}={\theta}T$ is automatically continuous.

• 대한수학회보
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• 제57권4호
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• pp.831-838
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• 2020

Let H be a complex Hilbert space and T : H → H be a bounded linear operator. Then T is said to be norm attaining if there exists a unit vector x₀ ∈ H such that ║Tx₀║ = ║T║. If for any closed subspace M of H, the restriction T|M : M → H of T to M is norm attaining, then T is called an absolutely norm attaining operator or 𝓐𝓝-operator. In this note, we discuss linear maps on B(H), which preserve the class of absolutely norm attaining operators on H.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.27-47
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• 2012

It has become apparent from the recent work by Choi et al. [3] on the nonlinear beam deflection problem, that analysis of the integral operator $\mathcal{K}$ arising from the beam deflection equation on linear elastic foundation is important. Motivated by this observation, we perform investigations on the eigenstructure of the linear integral operator $\mathcal{K}_l$ which is a restriction of $\mathcal{K}$ on the finite interval [$-l,l$]. We derive a linear fourth-order boundary value problem which is a necessary and sufficient condition for being an eigenfunction of $\mathcal{K}_l$. Using this equivalent condition, we show that all the nontrivial eigenvalues of $\mathcal{K}l$ are in the interval (0, 1/$k$), where $k$ is the spring constant of the given elastic foundation. This implies that, as a linear operator from $L^2[-l,l]$ to $L^2[-l,l]$, $\mathcal{K}_l$ is positive and contractive in dimension-free context.

• 충청수학회지
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• 제30권3호
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• pp.323-329
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• 2017

In this paper, by rigorous calculations, we consider $L^2({\mathbb{R}})-spectrum$ of linear differential operators with periodic coefficients. These operators are usually seen in linearization of nonlinear partial differential equations about spatially periodic traveling wave solutions. Here, by using the solution operator obtained from Floquet theory, we prove rigorously that $L^2({\mathbb{R}})-spectrum$ of the linear operator is determined by the eigenvalues of Floquet matrix.

• 충청수학회지
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• 제7권1호
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• pp.123-139
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• 1994

In this paper we are concerned with optimal control problems whose costs are quadratic and whose states are governed by linear delay differential equations and general boundary conditions. The basic new idea of this paper is to introduce a new class of linear operators in such a way that the state equation subject to a starting function can be viewed as an inhomogeneous boundary value problem in the new linear operator equation. In this way we avoid the usual semigroup theory treatment to the problem and use only linear operator theory.