• 충청수학회지
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• 제23권1호
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• pp.1-10
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• 2010

In this note, we investigate the infinitesimal generators of the transformation groups induced by the Fourier-Gauss and Fourier-Mehler transforms on white noise functionals.

• 대한수학회지
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• 제37권5호
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• pp.687-705
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• 2000

The main purpose of this paper is to study differentiable one-parameter groups and cosine families of operators acting on white noise functions and their associated infinitesimal generators. In particular, we prove the heredity of differentiable one-parameter group and cosine family of operators under the second quantization of the Cuchy problems for the first and second or der differential equations.

• 대한수학회보
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• 제44권3호
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• pp.419-428
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• 2007

The space of periodic Boehmians with $\Delta$-convergence is a complete topological algebra which is not locally convex. A family of Boehmians $\{T_\lambda\}$ such that $T_0$ is the identity and $T_{\lambda_1+\lambda_2}=T_\lambda_1*T_\lambda_2$ for all real numbers $\lambda_1$ and $\lambda_2$ is called a one-parameter group of Boehmians. We show that if $\{T_\lambda\}$ is strongly continuous at zero, then $\{T_\lambda\}$ has an exponential representation. We also obtain some results concerning the infinitesimal generator for $\{T_\lambda\}$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권1호
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• pp.31-39
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• 2011

Stone's theorem states that "A bounded linear operator A is infinitesimal generator of a $C_0$-group of unitary operators on a Hilbert space H if and only if iA is self adjoint". In this paper we establish a generalization of Stone's theorem in the framework of Hilbert $C^*$-modules.

• 전자공학회논문지
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• 제49권9호
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• pp.287-292
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• 2012

본 논문에서는 액체의 전기 전도도를 저잡음으로 검출하기 위하여 동기복조를 이용하는 전도도 검출기를 설계한다. 이를 위하여 검출기는 반송파 발생기, 전도도 검출 셀, 전류-전압 변환기 및 동기 복조기로 구성하며, 복조기의 대역폭을 조정하여 검출기의 신호 대 잡음비(SNR)를 개선함으로써, 액체의 극미한 전도도도 용이하게 측정할 수 있도록 한다. 이의 응용 예로써, 반도체 공정의 공기감시용 전도도 검출기를 동기복조를 이용하여 설계하며, 실험을 통하여 설계의 타당성을 확인한다. 실험 결과, 검출기는 설계 성능에 부합하는 특성을 나타내므로, 동기복조를 이용한 전도도 검출기는 액체의 극미한 전도도 측정에 유용하게 사용될 수 있음을 입증하였다.

• 대한수학회지
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• 제45권6호
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• pp.1785-1801
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• 2008

Noncommutative extensions of the Gross and Beltrami Laplacians, called the quantum Gross Laplacian and the quantum Beltrami Laplacian, resp., are introduced and their basic properties are studied. As noncommutative extensions of the Fourier-Gauss and Fourier-Mehler transforms, we introduce the quantum Fourier-Gauss and quantum Fourier- Mehler transforms. The infinitesimal generators of all differentiable one parameter groups induced by the quantum Fourier-Gauss transform are linear combinations of the quantum Gross Laplacian and quantum Beltrami Laplacian. A characterization of the quantum Fourier-Mehler transform is studied.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1987년도 한국자동제어학술회의논문집(한일합동학술편); 한국과학기술대학, 충남; 16-17 Oct. 1987
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• pp.729-733
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• 1987

Stability of Co Semigroups perturbed via the steady state Riccati equation (SSRE) is studied. We consider an infinite dimensional system : .chi. over dot = A.chi. + Bu, in, (A), domain of A, where A is the infinitesimal generator of a Co semigroup [T(t), t.geq.0] in H. If the original Co semigroup [T(t), t.geq.0] has a lower bound : vertical bar T(t).chi. vertical bar .geq. k vertical bar .chi. vertical bar, for all .chi. in H. t.geq. 0 and k>0, then the perturbed Co semigroup via the SSRE, where the feedback operator B is compact, cannot be exponentially stable. Physical interpretation of this result is as follows : in real applications, a finite number of actuators are available, therefore the operator B is compact. When the original system is inherently unstable, that is, has an infinite number of unstable modes, the perturbed system via the SSRE cannot be stable with a uniform decay rate.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권3호
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• pp.203-215
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• 2009

In this article, we study the existence and uniqueness of mild and classical solutions for a nonlinear impulsive differential equation with nonlocal conditions u'(t) = Au(t) + f(t, u(t); Tu(t); Su(t)), $0{\leq}t{\leq}T_0$, $t{\neq}t_i$, u(0) + g(u) = $u_0$, ${\Delta}u(t_i)=I_i(u(t_i))$, i = 1,2,${\ldots}$p, 0<$t_1$<$t_2$<$\cdots$<$t_p$<$T_0$, in a Banach space X, where A is the infinitesimal generator of a $C_0$ semigroup, g constitutes a nonlocal conditions, and ${\Delta}u(t_i)=u(t_i^+)-u(t_i^-)$ represents an impulsive conditions.

• 대한수학회보
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• 제23권2호
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• pp.167-170
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• 1986

Let M be a von Neumann algebra and .alpha., .betha. be *-automorphisms of M satisfying the operator equation .alpha.+.alpha.$^{-1}$ =.betha.+.betha.$^{-1}$ This operator equation has been extensively studied and many important decomposition theorems have been obtained by several authors (for instance see [4], [5], [2], [1]). Originally, this operator equation arose in the paper of Van Daele on the new approach of the Tomita-Takesaki theory in the case of modular operators ([7]). In the case of one-parameter automorphism groups, this equation has produced a bounded and completely positive map which can play a role similar to the infinitesimal generator (for details see [6] and [1]). A recent and one of the most important applications of this equation has been in developing an anglogue of the Tomita-Takesaki theory for Jordan algebras by Haagerup [3]. One general result of this theory is the following.