• Title, Summary, Keyword: linear operator

### A Linear Window Operator Based Upon the Algorithm Decomposition (알고리즘 분해방법을 이용한 Linear Window Operator의 구현)

• 정재길
• The Journal of Information Technology
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• v.5 no.1
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• pp.133-142
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• 2002
• This paper presents an efficient implementation of the linear window operator. I derived computational primitives based upon a block state space representation. The computational primitive can be implemented as a data path for a programmable processor, which can be used for the efficient implementation of a linear window operator. A multiprocessor architecture is presented for the realtime processing of a linear window operator. The architecture is designed based upon the data partitioning technique. Performance analysis for the various block size is provided.

### ABSTRACT RANDOM LINEAR OPERATORS ON PROBABILISTIC UNITARY SPACES

• Tran, Xuan Quy;Dang, Hung Thang;Nguyen, Thinh
• Journal of the Korean Mathematical Society
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• v.53 no.2
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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 . The representation theorem for abstract random bounded linear operators and some results on the adjoint of abstract random linear operators are given.

### LINEAR MAPS PRESERVING ����-OPERATORS

• Golla, Ramesh;Osaka, Hiroyuki
• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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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 ����-operator. In this note, we discuss linear maps on B(H), which preserve the class of absolutely norm attaining operators on H.

### THE MINIMUM MODULUS OF A LINEAR MAP IN OPERATOR SPACES

• Kye, Seung-Hyeok
• Communications of the Korean Mathematical Society
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• v.23 no.4
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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.

### Rank-preserver of Matrices over Chain Semiring

• Song, Seok-Zun;Kang, Kyung-Tae
• Kyungpook Mathematical Journal
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• v.46 no.1
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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.

### CONTINUITY OF LINEAR OPERATOR INTERTWINING WITH DECOMPOSABLE OPERATORS AND PURE HYPONORMAL OPERATORS

• Park, Sung-Wook;Han, Hyuk;Park, Se Won
• Journal of the Chungcheong Mathematical Society
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• v.16 no.1
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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.

### SPECTRAL ANALYSIS OF THE INTEGRAL OPERATOR ARISING FROM THE BEAM DEFLECTION PROBLEM ON ELASTIC FOUNDATION I: POSITIVENESS AND CONTRACTIVENESS

• Choi, Sung-Woo
• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.27-47
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• 2012
• It has become apparent from the recent work by Choi et al.  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.

### The Characterization of Optimal Control Using Delay Differential Operator

• Shim, Jaedong
• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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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.

### NOTE ON SPECTRUM OF LINEAR DIFFERENTIAL OPERATORS WITH PERIODIC COEFFICIENTS

• Jung, Soyeun
• Journal of the Chungcheong Mathematical Society
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• v.30 no.3
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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.