• 대한수학회보
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• 제26권1호
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• pp.11-17
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• 1989

In [1], Johnson and Lapidus introduced a family { $A_{t}$ :t>0} of Banach algebras of functionals on Wiener space and showed that for every F in $A_{t}$ , the analytic operator-valued function space integral $K_{\lambda}$$^{t}$ (F) exists for all nonzero complex numbers .lambda. with nonnegative real part. In [2,3] Johnson and Lapidus introduced a noncommtative multiplication having the property that if F.mem. $A_{t}$ $_{1}$ and G.mem. $A_{t}$ $_{2}$ then $F^{*}$G.mem. A$t_{1}$+$_{t}$ $_{2}$ and (Fig.) Note that for F, G in $A_{t}$ , $F^{*}$G is not in $A_{t}$ but rather is in $A_{2t}$ and so the multiplication * is not internal to the Banach algebra $A_{t}$ . In this paper we introduce an internal noncommutative multiplication on $A_{t}$ having the property that for F, G in $A_{t}$ , F G is in $A_{t}$ and (Fig.) for all nonzero .lambda. with nonnegative real part. Thus is an auxiliary binary operator on $A_{t}$ .TEX> .

• 한국학교수학회논문집
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• 제22권3호
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• pp.303-327
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• 2019

본 연구는 초등학교 수학에서 곱셈에 대한 학생들의 이해를 돕는 하나의 방안으로 곱셈의 통합적 접근을 제안하였다. 곱셈의 통합적 접근이란 수학 수업에서 학생들이 하나의 곱셈 상황을 다양한 방법으로 해결하고 서로의 방법에 대해 탐색하고 논의하면서 곱셈에 대해 폭넓은 이해를 하도록 하는 것이다. 곱셈의 통합적 접근은 곱셈에 대한 다양한 접근, 일관적 접근, 특정한 접근을 강조한 여러 선행 연구를 기반으로 도출되었다. 연구 결과, 곱셈의 통합적 접근은 하나의 곱셈 상황을 크게 4가지 방법으로 해석할 수 있으며 각각의 방법은 선행 연구에서 강조한 곱셈의 중요한 특성과 모두 연결된다. 또한, 곱셈의 통합적 접근은 곱셈뿐만 아니라 나눗셈, 분수 및 분수의 연산, 비와 비율, 비례 등으로 자연스럽게 확장되는 데 중요하다는 것을 이론적으로 확인하였다. 이를 통해 초등학교 수학에서 다루는 곱셈과 관련하여 실제 수업을 진행하는 교사에게 시사점을 제공하고자 한다.

• 대한수학회논문집
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• 제12권4호
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• pp.895-904
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• 1997

Let B(z) be a power series with operator coefficients where multiplication by B(z), T, is a contractive and everywhere defined transforamtion in the square summable power series. Then there is a Julia operator U for T such that $$ U = (T D)(\tilde{D}^* L) \in B(H \oplus D, K \oplus \tilde{D}), $$ where D is the state space of a conjugate canonical linear system with transfer function B(z).

• 대한수학회지
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• 제33권1호
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• pp.205-216
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• 1996

In [13], Ptak and Vrbova proved that if T is a bounded normal operator T on a complex Hilbert space H, then the ranges of the spectral projections can be represented in the form $$ \varepsilon(F)H = \bigcap_{\lambda\notinF} (T - \lambda I) H for all closed subsets F of C, $$ where $\varepsilon$ denotes the spectral measure associated with T.

• Kyungpook Mathematical Journal
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• 제49권1호
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• pp.31-39
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• 2009

Let $T_{\rho}$ be the generalized fractional integral operator associated to a function ${\rho}:(0,{\infty}){\rightarrow}(0,{\infty})$, as defined in [16]. For a function W on $\mathbb{R}^n$, we shall be interested in the boundedness of the multiplication operator $f{\mapsto}W{\cdot}T_{\rho}f$ on generalized Morrey spaces. Under some assumptions on ${\rho}$, we obtain an inequality for $W{\cdot}T_{\rho}$, which can be viewed as an extension of Olsen's and Kurata-Nishigaki-Sugano's results.

• 대한수학회논문집
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• 제36권3호
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• pp.465-483
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• 2021

Let 𝓗(𝔻) be the space of analytic functions on the unit disc 𝔻. Let 𝜓 = (𝜓_j)ⁿ_j=0 and 𝚽 = (𝚽_j)ⁿ_j=0 be such that 𝜓_j, 𝚽_j ∈ 𝓗(𝔻). The linear differential operator is defined by T_𝜓(f) = ∑ⁿ_j=0 𝜓_jf^(j), f ∈ 𝓗(𝔻). We characterize the boundedness and compactness of the difference operator (T_𝜓 - T_𝚽)(f) = ∑ⁿ_j=0 (𝜓_j - 𝚽_j) f^(j) between weighted-type spaces of analytic functions. As applications, we obtained boundedness and compactness of the difference of multiplication operators between weighted-type and Bloch-type spaces. Also, we give examples of unbounded (non compact) differential operators such that their difference is bounded (compact).

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2000년도 ITC-CSCC -2
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• pp.623-626
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• 2000

The purpose of this paper is to find an efficient solution for multiple constant multiplication (MCM) problem. Since the circuit structure can be represented as a directed acyclic graph, evolutionary computing is considered as an effective tool for optimization of circuit synthesis. In this paper, we propose a stack type operator as a chromosome element to synthesize a directed acyclic graph efficiently. This type of chromosome can represent a graph structure with a set of simple symbols and so we can employ the similar method to a conventional GA.

• 호남수학학술지
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• 제23권1호
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• pp.29-39
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• 2001

Let $\mathcal{B}$ be a Banach space of analytic functions defined on the open unit disk. Assume S is a bounded operator defined on $\mathcal{B}$ such that S is in the commutant of $M_zn$ or $SM_zn=-M_znS$ for some positive integer n. We give necessary and sufficient condition between compactness of $SM_z+cM_zS$ where c = 1, -1, i, -i, and the structure of S. Also we characterize the commutant of $M_zn$ for some positive integer n.

• 대한수학회보
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• 제44권4호
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• pp.701-708
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• 2007

In this paper we characterize the boundedness, compactness and closedness of the range of the weighted composition operators on Lorentz spaces L(p,q), $1.

• 대한수학회보
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• 제34권2호
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• pp.317-334
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• 1997

The existence of an operator-valued function space integral as an operator on $L_p(R) (1 \leq p \leq 2)$ was established for certain functionals which involved the Labesgue measure [1,2,6,7]. Johnson and Lapidus showed the existence of the integral as an operator on $L_2(R)$ for certain functionals which involved any Borel measures [5]. J. S. Chang and Johnson proved the existence of the integral as an operator from L_1(R)$ to $C_0(R)$ for certain functionals involving some Borel measures [3]. K. S. Chang and K. S. Ryu showed the existence of the integral as an operator from $L_p(R) to L_p'(R)$ for certain functionals involving some Borel measures [4].