• Korean Journal of Mathematics
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• 제29권3호
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• pp.511-518
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• 2021

In this paper, a relationship between the extended spectrum of the Aluthge transform and the extended spectrum of the operator T is proved. Other relationships between two different operators and other results are also given.

• 지구물리와물리탐사
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• 제2권1호
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• pp.54-62
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• 1999

본 논문은 파동장의 심도방향으로의 외삽(extrapolation)을 사용한 중합전 데이터밍 기법을 소개한다. 데이터밍 알고리즘의 유도를 위해, 우선 평면에 정의되어 있는 파동장을 임의의 굴곡을 갖는 면으로 외삽을 수행하는 모델링 연산자를 대수학적으로 구한 후, 이러한 모델링 연산자와 어드조인트(adjoint)관계에 있는 연산자를 대수학적으로 구하여 데이터밍 연산자를 얻게된다. 본 논문에서 사용된 취합전 모델링 연산자는 이미 널리 쓰이고 있는 중합전 마이그레이션(prestack migration) 중의 하나인 survey sinking 방법의 모델링에 해당하는 double square root(DSR)식이 사용되었다.

• 대한수학회보
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• 제33권2호
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• pp.233-241
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• 1996

The study of non-self-adjoint operator algebras on Hilbert space was only beginned by W.B. Arveson[1] in 1974. Recently, such algebras have been found to be of use in physics, in electrical engineering, and in general systems theory. Of particular interest to mathematicians are reflexive algebras with commutative lattices of invariant subspaces.

• 대한수학회지
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• 제39권4호
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• pp.559-577
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• 2002

It is known that the analytic operator-valued Feynman integral exists for some "potentials" which we so singular that they must be given by measures rather than by functions. Corresponding stability results involving monotonicity assumptions have been established by the author and others. Here in our main theorem we prove further stability theorem without monotonicity requirements.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제7권1호
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• pp.49-60
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• 2000

We will characterize isomorphisms from the adjoint of a certain tridiag-onal algebra $AlgL_{2n}$ onto $AlgL_{2n}$. In this paper the following are proved: A map $\Phi{\;}:{\;}(AlgL_{2n})^{*}{\;}{\longrightarrow}{\;}AlgL_{2n}$ is an isomorphism if and only if there exists an operator S in $AlgL_{2n}$ with all diagonal entries are 1 and an invertible backward diagonal operator B such that ${\Phi}(A){\;}={\;}SBAB^{-1}S^{-1}$.

• 호남수학학술지
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• 제26권4호
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• pp.455-462
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• 2004

We prove that if ${\mathbb{K}}^*$ is adjoint operator on $W_2{^2}({\Omega})$, then ${\mathbb{K}}^*v(t,\;{\tau})=,\;v(x,\;y){\in}W_2{^2}({\Omega})$ ; it is also related to the decomposition of solution of Fredholm equations.

• 대한수학회논문집
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• 제33권4호
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• pp.1249-1269
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• 2018

This paper provides a method to study the nonnegativity of certain linear operators, from other operators with similar spectral properties. If these new operators are formally self-adjoint and nonnegative, we can study the complex powers using an appropriate locally convex space. In this case, the initial operator also will be nonnegative and we will be able to study its powers. In particular, we have applied this method to Bessel-type operators.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권4호
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• pp.255-275
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• 2022

In this paper, we introduce a new system of set-valued variational inclusion problems in semi-inner product spaces. We use resolvent operator technique to propose an iterative algorithm for computing the approximate solution of the system of set-valued variational inclusion problems. The results presented in this paper generalize, improve and unify many previously known results in the literature.

• 대한수학회보
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• 제59권5호
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• pp.1215-1235
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• 2022

In this paper we study Szegö kernel projections for Hardy spaces in quaternionic Clifford analysis. At first we introduce the matrix Szegö projection operator for the Hardy space of quaternionic Hermitean monogenic functions by the characterization of the matrix Hilbert transform in the quaternionic Clifford analysis. Then we establish the Kerzman-Stein formula which closely connects the matrix Szegö projection operator with the Hardy projection operator onto the Hardy space, and we get the matrix Szegö projection operator in terms of the Hardy projection operator and its adjoint. At last, we construct the explicit matrix Szegö kernel function for the Hardy space on the sphere as an example, and get the solution to a Diriclet boundary value problem for matrix functions.

• 한국전산응용수학회:학술대회논문집
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• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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• pp.4.1-4
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• 2003

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX= Y. An interpolating operator for n-operators satisfies the equation AXi= Yi, for i = 1,2,...,n, In this article, we showed the following : Let H be a Hilbert space and let L be a subspace lattice on H. Let X and Y be operators acting on H. Assume that rangeX is dense in H. Then the following statements are equivalent : (1) There exists an operator A in AlgL such that AX = Y, A$\^$*/=A and every E in L reduces A. (2) sup｛(equation omitted) : n $\in$ N f$\sub$I/ $\in$ H and E$\sub$I/ $\in$ L｝<$\infty$ and = for all E in L and all f, g in H.