• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.643-656
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• 2009

The family of demi-linear mappings between topological vector spaces is a meaningful extension of the family of linear operators. We establish equicontinuity results for demi-linear mappings and develop the usual theory of distributions and the usual duality theory.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.185-190
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• 1989

In [4], J. Leray introduced the notion of partial hyperbolicity to characterize the operators for which the non-characteristic Cauchy problem is solvable in the Geverey class for any data which are holomorphic in a part of variables x"=(x$_{2}$,..,x$_{l}$ ) in the initial hyperplane x$_{1}$=0. A linear partial differential operator is called partially hyperbolic modulo the linear subvarieties S:x"=constant if the equation P$_{m}$(x, .zeta.$_{1}$, .xi.')=0 for .zeta.$_{1}$ has only real roots when .xi.'is real and .xi."=0, where P$_{m}$ is the principal symbol of pp. Limiting to the case of operators with constant coefficients, A. Kaneko proposed a new sharper condition when S is a hyperplane [3]. In this paper, we generalize this condition to the case of general linear subvariety S and show that it is sufficient for the solvability of Cauchy problem for the hyperfunction Cauchy data which contains variables parallel to S as holomorphic parameters.blem for the hyperfunction Cauchy data which contains variables parallel to S as holomorphic parameters.

• Korean Journal of Mathematics
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• v.15 no.2
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• pp.101-114
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• 2007

For an $m$ by $n$ nonnegative real matrix A, the maximal column rank of A is the maximal number of the columns of A which are linearly independent. In this paper, we analyze relationships between ranks and maximal column ranks of matrices over nonnegative reals. We also characterize the linear operators which preserve the maximal column rank of matrices over nonnegative reals.

• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.543-564
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• 1999

Consider a symmetric bilinear form defined on $\prod\times\prod$ by $_{\lambda\mu}$ = $<\sigma,fg>\;+\;\lambdaL[f](a)L[g](a)\;+\;\muM[f](b)m[g](b)$ ,where $\sigma$ is a quasi-definite moment functional, L and M are linear operators on $\prod$, the space of all real polynomials and a,b,$\lambda$ , and $\mu$ are real constants. We find a necessary and sufficient condition for the above bilinear form to be quasi-definite and study various properties of corresponding orthogonal polynomials. This unifies many previous works which treated cases when both L and M are differential or difference operators. finally, infinite order operator equations having such orthogonal polynomials as eigenfunctions are given when $\mu$=0.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.825-837
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• 2010

In this paper, we obtain a Korovkin type approximation theorem for double sequences of positive linear operators of two variables from $H_w$ (K) to C (K) via A-statistical convergence. Also, we construct an example such that our new approximation result works but its classical case does not work. Furthermore, we study the rates of A-statistical convergence by means of the modulus of continuity.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.113-123
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• 2009

A rank one matrix can be factored as $\mathbf{u}^t\mathbf{v}$ for vectors $\mathbf{u}$ and $\mathbf{v}$ of appropriate orders. The perimeter of this rank one matrix is the number of nonzero entries in $\mathbf{u}$ plus the number of nonzero entries in $\mathbf{v}$. A matrix of rank k is the sum of k rank one matrices. The perimeter of a matrix of rank k is the minimum of the sums of perimeters of the rank one matrices. In this article we characterize the linear operators that preserve perimeters of matrices over semirings.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.735-741
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• 2019

Let ${\mathcal{H}}$ be a complex Hilbert space and ${\mathcal{B}}({\mathcal{H}})$ the algebra of all bounded linear operators on ${\mathcal{H}}$. In this paper, we prove that if ${\varphi}:{\mathcal{B}}({\mathcal{H}}){\rightarrow}{\mathcal{B}}({\mathcal{H}})$ is a unital surjective bounded linear map, which preserves m- isometries m = 1, 2 in both directions, then there are unitary operators $U,V{\in}{\mathcal{B}}({\mathcal{H}})$ such that ${\varphi}(T)=UTV$ or ${\varphi}(T)=UT^{tr}V$ for all $T{\in}{\mathcal{B}}({\mathcal{H}})$, where $T^{tr}$ is the transpose of T with respect to an arbitrary but fixed orthonormal basis of ${\mathcal{H}}$.

• Journal of the Korean Mathematical Society
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• v.61 no.5
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• pp.1035-1050
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• 2024

The Cameron-Martin translation theorem describes how Wiener measure changes under translation by elements of the Cameron-Martin space in an abstract Wiener space (AWS). Translation theorems for the analytic Feynman integrals also have been established in the literature. In this article, we derive a more general translation theorem for the analytic Feynman integral associated with bounded linear operators (B.L.OP.) on AWSs. To do this, we use a certain behavior which exists between the analytic Fourier-Feynman transform (FFT) and the convolution product (CP) of functionals on AWS. As an interesting application, we apply this translation theorem to evaluate the analytic Feynman integral of the functional $$F(x)={\exp}\left(-iq\int_{0}^{T}x(t)y(t)dt\right),\,y{\in}C_0[0,\,T],\;q{\in}{\mathbb{R}}\,{\backslash}\,\{0\}$$ defined on the classical Wiener space C₀[0, T].

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.208-213
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• 1992

In this paper we are concerned with optimal control problems whose costs am quadratic and whose states are governed by linear delay 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.

• Kyungpook Mathematical Journal
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• v.27 no.2
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• pp.163-168
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• 1987