• 제목/요약/키워드: complex Hilbert space

검색결과 76건 처리시간 0.023초

UNITARY INTERPOLATION ON AX = Y IN A TRIDIAGONAL ALGEBRA ALG𝓛

  • JO, YOUNG SOO;KANG, JOO HO;PARK, DONGWAN
    • 호남수학학술지
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    • 제27권4호
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    • pp.649-654
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    • 2005
  • Given operators X and Y acting on a separable complex Hilbert space ${\mathcal{H}}$, an interpolating operator is a bounded operator A such that AX = Y. We show the following: Let $Alg{\mathcal{L}}$ be a subspace lattice acting on a separable complex Hilbert space ${\mathcal{H}}$ and let $X=(x_{ij})$ and $Y=(y_{ij})$ be operators acting on ${\mathcal{H}}$. Then the following are equivalent: (1) There exists a unitary operator $A=(a_{ij})$ in $Alg{\mathcal{L}}$ such that AX = Y. (2) There is a bounded sequence {${\alpha}_n$} in ${\mathbb{C}}$ such that ${\mid}{\alpha}_j{\mid}=1$ and $y_{ij}={\alpha}_jx_{ij}$ for $j{\in}{\mathbb{N}}$.

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Transient response of vibration systems with viscous-hysteretic mixed damping using Hilbert transform and effective eigenvalues

  • Bae, S.H.;Jeong, W.B.;Cho, J.R.;Lee, J.H.
    • Smart Structures and Systems
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    • 제20권3호
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    • pp.263-272
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    • 2017
  • This paper presents the time response of a mixed vibration system with the viscous damping and the hysteretic damping. There are two ways to derive the time response of such a vibration system. One is an analytical method, using the contour integral of complex functions to compute the inverse Fourier transforms. The other is an approximate method in which the analytic functions derived by Hilbert transform are expressed in the state space representation, and only the effective eigenvalues are used to efficiently compute the transient response. The unit impulse responses of the two methods are compared and the change in the damping properties which depend on the viscous and hysteretic damping values is investigated. The results showed that the damping properties of a mixed damping vibration system do not present themselves as a linear combination of damping properties.

힐버트 변환을 이용한 복소강성을 지니는 1자유도 시스템의 과도응답 (Transient Response of 1 DOF Complex Stiffness System via Hilbert-transform)

  • 배승훈;정의봉;조진래
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2014년도 추계학술대회 논문집
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    • pp.298-299
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    • 2014
  • The solution of transient response of complex stiffness system was obtained using a green function of this system. To derive the green function, governing equation of this systems was expressed in Steady Space and solved by the diagonalization. The solution of this system are written as a convolution integral form. The result that are calculated by the numerical integration process for transient responses was showed properly.

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A BERBERIAN TYPE EXTENSION OF FUGLEDE-PUTNAM THEOREM FOR QUASI-CLASS A OPERATORS

  • Kim, In Hyoun;Jeon, In Ho
    • Korean Journal of Mathematics
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    • 제16권4호
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    • pp.583-587
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    • 2008
  • Let $\mathfrak{L(H)}$ denote the algebra of bounded linear operators on a separable infinite dimensional complex Hilbert space $\mathfrak{H}$. We say that $T{\in}\mathfrak{L(H)}$ is a quasi-class A operator if $$T^*{\mid}T^2{\mid}T{{\geq}}T^*{\mid}T{\mid}^2T$$. In this paper we prove that if A and B are quasi-class A operators, and $B^*$ is invertible, then for a Hilbert-Schmidt operator X $$AX=XB\;implies\;A^*X=XB^*$$.

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ON STRUCTURES OF CONTRACTIONS IN DUAL OPERATOR ALGEBRAS

  • Kim, Myung-Jae
    • 대한수학회논문집
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    • 제10권4호
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    • pp.899-906
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    • 1995
  • We discuss certain structure theorems in the class A which is closely related to the study of the problems of solving systems concerning the predual of a dual operator algebra generated by a contraction on a separable infinite dimensional complex Hilbert space.

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ON A DECOMPOSITION OF MINIMAL COISOMETRIC EXTENSIONS

  • Park, Kun-Wook
    • 대한수학회논문집
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    • 제9권4호
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    • pp.847-852
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    • 1994
  • Let $H$ be a separable, infinite dimensional, complex Hilbert space and let $L(H)$ be the algebra of all bounded linear operator on $H$. A dual algebra is a subalgebra of $L(H)$ that contains the identity operator $I_H$ and is closed in the ultraweak operator topology on $L(H)$.

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