• 대한수학회보
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• 제38권1호
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• pp.17-27
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• 2001

We discuss a finite difference preconditioner for the$C^1$ Lagrance quadratic spline collocation method for a uniformly elliptic operator with homogeneous Dirichlet boundary conditions. Using the generalized field of values argument, we analyzed eigenvalues of the matrix preconditioned by the matrix corresponding to a finite difference operator with zero boundary condition.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권4호
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• pp.315-328
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• 2021

A characterization of frame operators of finite Gabor frames is presented here. Regularity aspects of Gabor frames in 𝑙²(ℤ_N) are discussed by introducing associated semi-frame operators. Gabor type frames in finite dimensional Hilbert spaces are also introduced and discussed.

• 대한수학회보
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• 제48권6호
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• pp.1129-1135
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• 2011

In this note, we prove that every subscalar operator with finite spectrum is algebraic. In particular, a quasi-nilpotent subscala operator is nilpotent. We also prove that every subscalar operator with property (${\delta}$) on a Banach space of dimension greater than 1 has a nontrivial invariant closed linear subspace.

• 충청수학회지
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• 제23권2호
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• pp.305-313
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• 2010

In this paper, we prove that if $T{\in}L$(X) is a generalized scalar operator then Ker $T^p$ is the quasi-nilpotent part of T for some positive integer $p{\in}{\mathbb{N}}$. Moreover, we prove that a generalized scalar operator with finite spectrum is algebraic. In particular, a quasi-nilpotent generalized scalar operator is nilpotent.

• 대한수학회지
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• 제47권2호
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• pp.223-233
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• 2010

In this paper, we use q-differential operator to recover the finite Heine $_2\Phi_1$ transformations given in [3]. Applying that, we also obtain some terminating q-series transformation formulas.

• 충청수학회지
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• 제26권1호
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• pp.181-190
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• 2013

In this paper we study the Putinar's matricial model operator of rank 2 and provide some evidences for the validity of the conjecture in [8].

• 대한수학회논문집
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• 제9권3호
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• pp.593-598
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• 1994

In this note we give some results on the jump (due to Kato [5] and West [7]) of a semi-Fredholm operator. Throughout this note, suppose X is an Banach space and write L(X) for the set of all bounded linear operators on X. A operator $T \in L(x)$ is called upper semi-Fredholm if it has closed range with finite dimensional null space, and lower semi-Fredholm if it has closed range with its range of finite co-dimension. It T is either upper or lower semi-Fredholm we shall call it semi-Fredholm and Fredholm it is both. The index of a (semi-) Fredholm operator T is given by $$ index(T) = n(T) = d(T),$$ where $n(T) = dim T^{-1}(0)$ and d(T) = codim T(X).

• 대한수학회지
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• 제52권6호
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• pp.1337-1346
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• 2015

We examine the relationship of the shape operator of a surface of Euclidean 3-space with its Gauss map of pointwise 1-type. Surfaces with constant mean curvature and right circular cones with respect to some properties of the shape operator are characterized when their Gauss map is of pointwise 1-type.

• 대한수학회논문집
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• 제28권2호
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• pp.285-295
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• 2013

In this note we present sufficient conditions for the existence of Radon-Nikodym derivatives (RND) of operator valued measures with respect to scalar measures. The RND is characterized by the Bochner integral in the strong operator topology of a strongly measurable operator valued function with respect to a nonnegative finite measure. Using this result we also obtain a characterization of compact sets in the space of operator valued measures. An extension of this result is also given using the theory of Pettis integral. These results have interesting applications in the study of evolution equations on Banach spaces driven by operator valued measures as structural controls.

• East Asian mathematical journal
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• 제27권1호
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• pp.11-21
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• 2011

In this paper, we try to extend the viscosity approximation technique to find a particular common zero of a finite family of accretive mappings in a Banach space which is strictly convex reflexive and has a weakly sequentially continuous duality mapping. The explicit viscosity approximation scheme is proposed and its strong convergence to a solution of a variational inequality is proved.