• 대한수학회보
• /
• 제60권1호
• /
• pp.161-170
• /
• 2023

We consider dual Toeplitz operators acting on the orthogonal complement of the Dirichlet space on the unit disk. We give a characterization of when a finite sum of products of two dual Toeplitz operators is equal to 0. Our result extends several known results by using a unified way.

• 호남수학학술지
• /
• 제44권4호
• /
• pp.618-627
• /
• 2022

On the setting of the orthogonal complement of the weighted Bergman space, we study the problem of when a finite sum of dual Toeplitz products is compact or zero. Our results extend several known results on the unweighted space to the weighted spaces.

• 호남수학학술지
• /
• 제43권4호
• /
• pp.691-700
• /
• 2021

In this paper, we compute directly the Hankel matrix representation of the Hankel operator on the Hardy space of the unit disc without using any classical kernel functions with respect to special orthonormal bases for the Hardy space and its orthogonal complement. This gives an elementary proof for the formula.

• Korean Journal of Mathematics
• /
• 제27권4호
• /
• pp.977-1003
• /
• 2019

Let 𝓐 and 𝓑 be two unital C^⁎-algebras and 𝓐 ⊗ 𝓑 be their algebraic tensor product. For two bilinear maps on 𝓐 and 𝓑 with some specific conditions, we derive a bilinear map on 𝓐 ⊗ 𝓑 and study some characteristics. Considering two 𝓐 ⊗ 𝓑 bimodules, a centralizer is also obtained for 𝓐 ⊗ 𝓑 corresponding to the given bilinear maps on 𝓐 and 𝓑. A relationship between orthogonal complements of subspaces of 𝓐 and 𝓑 and their tensor product is also deduced with suitable example.

• 대한수학회지
• /
• 제45권6호
• /
• pp.1705-1723
• /
• 2008

Let n be a 2-step nilpotent Lie algebra which has an inner product <, > and has an orthogonal decomposition $n\;=z\;{\oplus}v$ for its center z and the orthogonal complement v of z. Then Each element z of z defines a skew symmetric linear map $J_z\;:\;v\;{\longrightarrow}\;v$ given by <$J_zx$, y> = for all x, $y\;{\in}\;v$. In this paper we characterize Jacobi fields and calculate all conjugate points of a simply connected 2-step nilpotent Lie group N with its Lie algebra n satisfying $J^2_z$ = A for all $z\;{\in}\;z$, where S is a positive definite symmetric operator on z and A is a negative definite symmetric operator on v.

• Journal of applied mathematics & informatics
• /
• 제26권5_6호
• /
• pp.1207-1214
• /
• 2008

We give an elementary proof of one of the main results in [H.O. Kim, R.Y. Kim, J.K. Lim, The infimum cosine angle between two finitely generated shift-invariant spaces and its applications, Appl. Comput. Har-mon. Anal. 19 (2005) 253-281] concerning the existence of an oblique projection onto a finitely generated shift-invariant space along the orthogonal complement of another finitely generated shift-invariant space under the assumption that the generators generate Riesz bases.

• 대한수학회논문집
• /
• 제27권1호
• /
• pp.185-195
• /
• 2012

We study the geometry of lightlike hypersurfaces M of an inde nite cosymplectic manifold $\bar{M}$ such that either (1) the characterist vector field $\zeta$ of $\bar{M}$ belongs to the screen distribution S(TM) of M or (2) $\zeta$ belongs to the orthogonal complement $S(TM)^{\perp}$ of S(TM) in $T\bar{M}$.

• 대한수학회지
• /
• 제57권4호
• /
• pp.973-986
• /
• 2020

In this paper, we compute the Hankel matrix representation of the Hankel operator on the Hardy space of a general bounded domain with respect to special orthonormal bases for the Hardy space and its orthogonal complement. Moreover we obtain the compact form of the Hankel matrix for the unit disc case with respect to these bases. One can see that the Hankel matrix generated by this computation turns out to be a generalization of the case of the unit disc from the single simply connected domain to multiply connected domains with much diversities of bases.

• 한국정보통신학회논문지
• /
• 제11권9호
• /
• pp.1734-1741
• /
• 2007

본 논문에서는 정규화 된 부반송파 간격과 확산 이득이 동일하고 각 부반송파의 직접 확산 코드가 직교하도록 하는 직교 MC DS-CDMA 시스템에 비트 동기와 위상 동기가 요구되지 않는 Hybrid SC/MRC-2/4 방식을 적용하였다. 다중 반송파 전송이 사용되는 광대역 무선 시스템에서는 가장 높은 부반송파 주파수와 가장 낮은 부반송파 주파수 차이 때문에 발생하는 도플러 주파수 천이가 발생하고 이로 인한 위상 에러율 보상하기 위하여 전체 시스템에 맞는 PLL이득 값을 조절하여 완전 동기 된 수신 신호가 되도록 직교 MC DS-CDMA시스템을 분석하였다. 분석 결과, PLL이득 값을 증가시킴에 따라 완전 동기 된 경우에 근접함을 알 수 있지만 일정 값 이상에서는 그 간격의 변화가 매우 작아짐을 알 수 있다. 따라서 시스템에 맞는 적절한 PLL이득 값을 선택함으로써 Hybrid SC/MRC 방식이 적용된 직교 MC DS-CDMA시스템을 설계할 수 있을 것이다.

• East Asian mathematical journal
• /
• 제22권2호
• /
• pp.249-257
• /
• 2006

Let n be a 2-step nilpotent Lie algebra which has an inner product <,> and has an orthogonal decomposition $n=\delta{\oplus}\varsigma$ for its center $\delta$ and the orthogonal complement $\varsigma\;of\;\delta$. Then Each element Z of $\delta$ defines a skew symmetric linear map $J_Z:\varsigma{\rightarrow}\varsigma$ given by $=$ for all $X,\;Y{\in}\varsigma$. Let $\gamma$ be a unit speed geodesic in a 2-step nilpotent Lie group H(2, 1) with its Lie algebra n(2, 1) and let its initial velocity ${\gamma}$(0) be given by ${\gamma}(0)=Z_0+X_0{\in}\delta{\oplus}\varsigma=n(2,\;1)$ with its center component $Z_0$ nonzero. Then we showed that $\gamma(0)$ is conjugate to $\gamma(\frac{2n{\pi}}{\theta})$, where n is a nonzero intger and $-{\theta}^2$ is a nonzero eigenvalue of $J^2_{Z_0}$, along $\gamma$ if and only if either $X_0$ is an eigenvector of $J^2_{Z_0}$ or $adX_0:\varsigma{\rightarrow}\delta$ is not surjective.