• 대한수학회논문집
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• 제33권3호
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• pp.853-869
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• 2018

We give a new characterization of Browder's theorem through equality between the pseudo B-Weyl spectrum and the generalized Drazin spectrum. Also, we will give conditions under which pseudo B-Fredholm and pseudo B-Weyl spectrum introduced in [9] and [25] become stable under commuting Riesz perturbations.

• 대한수학회보
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• 제57권2호
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• pp.509-520
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• 2020

We study the Toeplitz operators on the holomorphic and pluriharmonic Dirichlet spaces of the polydisk in terms of when Toeplitz operator is Fredholm operator there. Consequently, we describe the essential spectrum of Toeplitz operators.

• Kyungpook Mathematical Journal
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• 제45권4호
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• pp.471-480
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• 2005

This paper deals with some useful methods of solving the one-dimensional integral equation of Fredholm type. Application of the reduction techniques with a view to inverting a class of integral equation with Lauricella function in the kernel, Riemann-Liouville fractional integral operators as well as Weyl operators have been made to reduce to this class to generalized Stieltjes transform and inversion of which yields solution of the integral equation. Use of Mellin transform technique has also been made to solve the Fredholm integral equation pertaining to certain polynomials and H-functions.

• 대한전자공학회논문지
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• 제22권5호
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• pp.83-86
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• 1985

Fredholm 제 2종 적분 방정식의 수치해법에 관한 새로운 기범을 제시하였다. 문제 영역의 절점에 데이터를 혼합 형태로 가함으로써 근사해를 구하였다. 수치 해법에서 오차를 줄이기 위하여 모든 절정에서 2번 연속 미분가능한 cubic B-spline 함수를 기저함수로 사용하였다. 기저함수로서 cubit B-spline 함수를 이용한 본 기법의 결과와 기저함수로 pulse 함수 test 함수로는 delta 함수를 이용한 모멘트법의 결과를 예제를 통하여 비교하였다. 또한 이 방법에 대한 수렴 조건을 기술 하였다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권2호
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• pp.133-138
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• 2004

In this paper we derive a decomposition of the solution of Fredholm equations of the second kind in terms of reproducing kernels in the space ${W_2}^2$($\Omega$)

• 대한수학회보
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• 제53권3호
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• pp.681-698
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• 2016

In this paper, we investigate relative essential spectra of $2{\times}2$ block operator matrix using the Fredholm perturbation theory. Furthermore, an example for two-group transport equations is presented to illustrate the validity of the main results.

• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.801-812
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• 2000

Two-dimensional slow viscous flow on infinite half-plane past a perpendicular infinite cavity is considered on the basis of the Stokes approximation. Using complex representation of the two-dimensional Stokes flow, the problem is reduced to solving a set of Fredholm integral equations of the second kind. The streamlines and the pressure and vorticity distribution on the wall are numerically determined.

• 대한수학회보
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• 제59권1호
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• pp.1-13
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• 2022

The main aim of the article is to introduce new generalizations of Fredholm and Browder classes of spectra when the underlying Hilbert space is not necessarily separable and study their properties. To achieve the goal the notions of 𝛼-Browder operators, 𝛼-B-Fredholm operators, 𝛼-B-Browder operators and 𝛼-Drazin invertibility have been introduced. The relation of these classes of operators with their corresponding weighted spectra has been investigated. An equivalence of 𝛼-Drazin invertible operators with 𝛼-Browder operators and 𝛼-B-Browder operators has also been established. The weighted Browder spectrum of the sum of two bounded linear operators has been characterised in the case when the Hilbert space (not necessarily separable) is a direct sum of its closed invariant subspaces.

• 대한기계학회논문집
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• 제15권5호
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• pp.1611-1619
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• 1991

본 연구에서는 Hilton과 Sih의 경우를 확장 적용하여 Fig. 1(b)와 같이 탄성 층 내부에 존재하는 중앙균열선단의 응력확대계수 산출을 위하여 균열부위를 제외하고 는 섬유층과 레진층이 완전히 접착되었다고 가정한 모델을 다음과 같이 설정하였다. 중앙균열을 내재하고 있는 복합재료의 역학적 거동을 해석하기 위하여, 접착레진을 주 로하는 층(resin rich layer)을 중심으로 하여 상하 각1개의 섬유 (fiber)층과 균질한 특성을 갖는 복합재료의 층으로 단순화 하였으며, 이러한 단순화는 적층재에서의 균열 주위의 국부응력을 해석하기 위한 것으로서 복합재료는 레진층이나 섬유층에 비하여 매우 두꺼우므로 반무한체로 이상화 하였다. 선형탄성 이론에 의하여 혼합 경계조건 문제(mixed boundary value problem)로 부터 제2종 Fredholm적분방정식(fredholm int- egral equation of a second kind)을 유도하였으며 수치해석적인 방법에 의하여 응력 확대계수를 구하였다.

• 대한수학회보
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• 제55권5호
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• pp.1351-1370
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• 2018

In the first part of this paper we show that, under some conditions, a polynomially demicompact operator can be demicompact. An example involving the Caputo fractional derivative of order ${\alpha}$ is provided. Furthermore, we give a refinement of the left and the right Weyl essential spectra of a closed linear operator involving the class of demicompact ones. In the second part of this work we provide some sufficient conditions on the inputs of a closable block operator matrix, with domain consisting of vectors which satisfy certain conditions, to ensure the demicompactness of its closure. Moreover, we apply the obtained results to determine the essential spectra of this operator.