• Title/Summary/Keyword: multiplication operator

Search Result 57, Processing Time 0.026 seconds

POSINORMAL TERRACED MATRICES

  • Rhaly, H. Crawford, Jr.
    • Bulletin of the Korean Mathematical Society
    • /
    • v.46 no.1
    • /
    • pp.117-123
    • /
    • 2009
  • This paper is a study of some properties of a collection of bounded linear operators resulting from terraced matrices M acting through multiplication on ${\ell}^2$; the term terraced matrix refers to a lower triangular infinite matrix with constant row segments. Sufficient conditions are found for M to be posinormal, meaning that $MM^*=M^*PM$ for some positive operator P on ${\ell}^2$; these conditions lead to new sufficient conditions for the hyponormality of M. Sufficient conditions are also found for the adjoint $M^*$ to be posinormal, and it is observed that, unless M is essentially trivial, $M^*$ cannot be hyponormal. A few examples are considered that exhibit special behavior.

ON THE COMMUTANT OF MULTIPLICATION OPERATORS WITH ANALYTIC POLYNOMIAL SYMBOLS

  • Robati, B. Khani
    • Bulletin of the Korean Mathematical Society
    • /
    • v.44 no.4
    • /
    • pp.683-689
    • /
    • 2007
  • Let $\mathcal{B}$ be a certain Banach space consisting of analytic functions defined on a bounded domain G in the complex plane. Let ${\varphi}$ be an analytic polynomial or a rational function and let $M_{\varphi}$ denote the operator of multiplication by ${\varphi}$. Under certain condition on ${\varphi}$ and G, we characterize the commutant of $M_{\varphi}$ that is the set of all bounded operators T such that $TM_{\varphi}=M_{\varphi}T$. We show that $T=M_{\Psi}$, for some function ${\Psi}$ in $\mathcal{B}$.

GENERALIZED BOUNDED ANALYTIC FUNCTIONS IN THE SPACE Hω,p

  • Lee, Jun-Rak
    • Korean Journal of Mathematics
    • /
    • v.13 no.2
    • /
    • pp.193-202
    • /
    • 2005
  • We define a general space $H_{{\omega},p}$ of the Hardy space and improve that Aleman's results to the space $H_{{\omega},p}$. It follows that the multiplication operator on this space is cellular indecomposable and that each invariant subspace contains nontrivial bounded functions.

  • PDF

Correction and further improvements of Montgomery Modular Multiplier (수정 및 보다 향상된 성능의 몽고메리 모듈러 곱셈기 제안)

  • 신준범;이광형
    • Proceedings of the Korean Information Science Society Conference
    • /
    • 2000.10a
    • /
    • pp.590-592
    • /
    • 2000
  • Operator-level optimization of a systolic array for Montgomery Modular Multiplication(MMM) algorithm is presented in thin paper. The proposed systolic array is faster than that of C.D. Walter by 40%. Compared with J.B. Shin et al.'s, it is 25% faster.

  • PDF

Space Deformation of Parametric Surface Based on Extension Function

  • Wang, Xiaoping;Ye, Zhenglin;Meng, Yaqin;Li, Hongda
    • International Journal of CAD/CAM
    • /
    • v.1 no.1
    • /
    • pp.23-32
    • /
    • 2002
  • In this paper, a new technique of space deformation for parametric surfaces with so-called extension function (EF) is presented. Firstly, a special extension function is introduced. Then an operator matrix is constructed on the basis of EF. Finally the deformation of a surface is achieved through multiplying the equation of the surface by an operator matrix or adding the multiplication of some vector and the operator matrix to the equation. Interactively modifying control parameters, ideal deformation effect can be got. The implementation shows that the method is simple, intuitive and easy to control. It can be used in such fields as geometric modeling and computer animation.

A Study on the Theoretical Background of the Multiplication of Rational Numbers as Composition of Operators (두 조작의 합성으로서의 유리수 곱의 이론적 배경 고찰)

  • Choi, Keunbae
    • East Asian mathematical journal
    • /
    • v.33 no.2
    • /
    • pp.199-216
    • /
    • 2017
  • A rational number as operator is eventually that it is considered a mapping. Depending on how selecting domain (the target of operation by rational number) and codomain (including the results of operations by rational number), it is possible to see the rational in two aspects. First, rational numbers can be deal with functions if we choose the target of operation by rational number as a number field containing rationals. On the other hand, if we choose the target of operation by rational number as integral domain $\mathbb{Z}$, then rational numbers can be regarded as partial functions on $\mathbb{Z}$. In this paper, we regard the rational numbers with a view of partial functions, we investigate the theoretical background of the relationship between the multiplication of rational numbers and the composition of rational numbers as operators.

ON THE HILBERT SPACE OF FORMAL POWER SERIES

  • YOUSEFI, Bahman;SOLTANI, Rahmat
    • Honam Mathematical Journal
    • /
    • v.26 no.3
    • /
    • pp.299-308
    • /
    • 2004
  • Let $\{{\beta}(n)\}^{\infty}_{n=0}$ be a sequence of positive numbers such that ${\beta}(0)=1$. We consider the space $H^2({\beta})$ of all power series $f(z)=^{Po}_{n=0}{\hat{f}}(n)z^n$ such that $^{Po}_{n=0}{\mid}{\hat{f}}(n){\mid}^2{\beta}(n)^2<{\infty}$. We link the ideas of subspaces of $H^2({\beta})$ and zero sets. We give some sufficient conditions for a vector in $H^2({\beta})$ to be cyclic for the multiplication operator $M_z$. Also we characterize the commutant of some multiplication operators acting on $H^2({\beta})$.

  • PDF

Fast Mask Operators for the edge Detection in Vision System (시각시스템의 Edge 검출용 고속 마스크 Operator)

  • 최태영
    • The Journal of Korean Institute of Communications and Information Sciences
    • /
    • v.11 no.4
    • /
    • pp.280-286
    • /
    • 1986
  • A newmethod of fast mask operators for edge detection is proposed, which is based on the matrix factorization. The output of each component in the multi-directional mask operator is obtained adding every image pixels in the mask area weighting by corresponding mask element. Therefore, it is same as the result of matrix-vector multiplication like one dimensional transform, i, e, , trasnform of an image vector surrounded by mask with a transform matrix consisted of all the elements of eack mask row by row. In this paper, for the Sobel and Prewitt operators, we find the transform matrices, add up the number of operations factoring these matrices and compare the performances of the proposed method and the standard method. As a result, the number of operations with the proposed method, for Sobel and prewitt operators, without any extra storage element, are reduced by 42.85% and 50% of the standard operations, respectively and in case of an image having 100x100 pixels, the proposed Sobel operator with 301 extra storage locations can be computed by 35.93% of the standard method.

  • PDF

GALKIN'S LOWER BOUND CONJECURE FOR LAGRANGIAN AND ORTHOGONAL GRASSMANNIANS

  • Cheong, Daewoong;Han, Manwook
    • Bulletin of the Korean Mathematical Society
    • /
    • v.57 no.4
    • /
    • pp.933-943
    • /
    • 2020
  • Let M be a Fano manifold, and H🟉(M; ℂ) be the quantum cohomology ring of M with the quantum product 🟉. For 𝜎 ∈ H🟉(M; ℂ), denote by [𝜎] the quantum multiplication operator 𝜎🟉 on H🟉(M; ℂ). It was conjectured several years ago [7,8] and has been proved for many Fano manifolds [1,2,10,14], including our cases, that the operator [c1(M)] has a real valued eigenvalue 𝛿0 which is maximal among eigenvalues of [c1(M)]. Galkin's lower bound conjecture [6] states that for a Fano manifold M, 𝛿0 ≥ dim M + 1, and the equality holds if and only if M is the projective space ℙn. In this note, we show that Galkin's lower bound conjecture holds for Lagrangian and orthogonal Grassmannians, modulo some exceptions for the equality.

REPRODUCING KERNEL KREIN SPACES

  • Yang, Mee-Hyea
    • Journal of applied mathematics & informatics
    • /
    • v.8 no.2
    • /
    • pp.659-668
    • /
    • 2001
  • Let S(z) be a power series with operator coefficients such that multiplication by S(z) is an everywhere defined transformation in the square summable power series C(z). In this paper we show that there exists a reproducing kernel Krein space which is state space of extended canonical linear system with transfer function S(z). Also we characterize the reproducing kernel function of the state space of a linear system.