• 대한수학회지
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• 제48권6호
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• pp.1203-1223
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• 2011

In this paper, the authors investigate the structure of operators similar to normaloid and transloid operators. In particular, we characterize the interior of the set of operators similar to normaloid (transloid, respectively) operators. This gives a concise spectral condition to determine when an operator is similar to a normaloid or transloid operator. Also it is proved that any Hilbert space operator has a compact perturbation with transloid property. This is used to give a negative answer to a problem posed by W. Y. Lee, concerning Weyl's theorem.

• 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.

• 대한수학회보
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• 제54권1호
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• pp.215-223
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• 2017

In this paper, we establish results about operators similar to their adjoints. This is carried out in the setting of bounded and also unbounded operators on a Hilbert space. Among the results, we prove that an unbounded closed operator similar to its adjoint, via a cramped unitary operator, is self-adjoint. The proof of this result works also as a new proof of the celebrated result by Berberian on the same problem in the bounded case. Other results on similarity of hyponormal unbounded operators and their self-adjointness are also given, generalizing well known results by Sheth and Williams.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.515-523
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• 2019

The aim of this paper is to present some necessary and sufficient conditions for existence of solution of Sylvester operator equation involving bounded subnormal operators in a Hilbert space. Our results improve and generalize some results in the literature involving normal operators.

• East Asian mathematical journal
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• 제21권2호
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• pp.191-203
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• 2005

In the present paper we first establish some basic results for a substantially more general class of functions defined below. The results include simple differentiation and fractional calculus operators(integration and differentiation of arbitrary orders) for this class of functions. These results are then invoked in determining similar properties for the generalized Wright's hypergeometric functions. Further, norm estimate of a certain class of integral operators whose kernel involves the generalized Wright's hypergeometric function, and its composition(and other related properties) with the fractional calculus operators are also investigated.

• 충청수학회지
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• 제33권4호
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• pp.489-495
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• 2020

We define new integral operators on the Haydy space similar to Szegö projection. We consider a relationship between these Szegö type operators and the partial sum of Taylor series on the Hardy space.

• Kyungpook Mathematical Journal
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• 제60권2호
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• pp.297-305
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• 2020

We show that selfadjoint operator extensions of minimal second order difference operators have only discrete spectrum when the odd order coefficient is unbounded but grows or decays according to specific conditions. Selfadjoint operator extensions of minimal differential operator under similar growth and decay conditions on the coefficients have a absolutely continuous spectrum of multiplicity one.

• Structural Engineering and Mechanics
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• 제45권4호
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• pp.495-519
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• 2013

This paper investigates properties of integral operators in complex variable boundary integral equation in plane elasticity, which is derived from the Somigliana identity in the complex variable form. The generalized Sokhotski-Plemelj's formulae are used to obtain the BIE in complex variable. The properties of some integral operators in the interior problem are studied in detail. The Neumann and Dirichlet problems are analyzed. The prior condition for solution is studied. The solvability of the formulated problems is addressed. Similar analysis is carried out for the exterior problem. It is found that the properties of some integral operators in the exterior boundary value problem (BVP) are quite different from their counterparts in the interior BVP.

• 대한수학회지
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• 제58권1호
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• pp.91-107
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• 2021

A bounded linear operator T on a separable infinite dimensional Banach space X is called strongly hypercyclic if $$X{\backslash}\{0\}{\subseteq}{\bigcup_{n=0}^{\infty}}T^n(U)$$ for all nonempty open sets U ⊆ X. We show that if T is strongly hypercyclic, then so are Tn and cT for every n ≥ 2 and each unimodular complex number c. These results are similar to the well known Ansari and León-Müller theorems for hypercyclic operators. We give some results concerning multiplication operators and weighted composition operators. We also present a result about the invariant subset problem.

• 한국산학기술학회논문지
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• 제11권12호
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• pp.5042-5048
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• 2010

유비쿼터스 환경에서 다양한 센서로부터 생성되는 데이터 스트림에 대해 사용자가 요구하는 위치 기반 서비스를 효과적으로 지원하기 위해 연산자 네트워크와 공유 등을 통한 연속 질의 처리 기법이 활용되고 있다. 위치 정보 기반의 연속 질의 처리는 특정 영역을 중심으로 유사 질의가 집중적으로 발생할 수 있으므로, 본 논문에서는 유사한 조건을 갖는 공간 연산을 공유하기 위해 그리드 영역 분할을 이용한 공간 연산 공유 기법을 제안한다. 제안기법은 공간 연산을 직접 공유하지 않고 그리드 셀 별로 이동객체를 공유하기 때문에 유사한 조건을 갖는 공간 연산의 공유가 가능하여 공간 연산의 실행 빈도수를 크게 감소시켜 질의 처리 속도의 향상과 함께 메모리 이용률을 향상시킨다.