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On the Hyers-Ulam stability of the Banach space-valued differential equation y' = lambda y
Sin-Ei Takahasi,Takeshi Miura,Shizuo Miyajima 대한수학회 2002 대한수학회보 Vol.39 No.2
Let I be an open interval and X a complex Banach space.Let varepsilon geq 0 and lambda a non-zero complexnumber with text{rm Re},lambda neq 0. If varphi is astrongly differentiable map from I to X with Vertvarphi'(t)-lambda varphi(t) Vert leq varepsilon for allt in I, then we show that the distance between varphi and the set ofall solutions to the differential equation y' = lambda y is at mostvarepsilon/ vert text{rm Re},lambda vert.
ON THE HYERS-ULAM STABILITY OF THE BANACH SPACE-VALUED DIFFERENTIAL EQUATION y'=λy
Takahasi, Sin-Ei,Miura, Takeshi,Miyajima, Shizuo Korean Mathematical Society 2002 대한수학회보 Vol.39 No.2
Let I be an open interval and X a complex Banach space. Let$\varepsilon\geq0\;and\;\lambda$ a non-zero complex number with Re $\lambda\neq0$. If $\varphi$ is a strongly differentiable map from I to X with $\parallel\varphi^'(t)-\lambda\varphi(t)\parallel\leq\varepsilon\;for\;all\;t\in\;I$, then we show that the distance between $\varphi$ and the set of all solutions to the differential equation y'=$\lambda$y is at most $\varepsilon/$\mid$Re\lambda$\mid$$.
SPATIAL NUMERICAL RANGES OF ELEMENTS OF $C^*$-ALGEBRAS
Takahasi, Sin-Ei Korean Mathematical Society 2000 대한수학회보 Vol.37 No.3
When A is a subalgebra of a $C^*$-algebra, the spatial numerical range of element of A can be described in terms of positive linear functionals on the $C^*$-algebra.
Jyunji Inoue,Sin-Ei Takahasi 대한수학회 2022 대한수학회지 Vol.59 No.2
Let $G$ be a non-discrete locally compact abelian group, and $\mu$ be a transformable and translation bounded Radon measure on $G$. In this paper, we construct a Segal algebra $S_{\mu}(G)$ in $L^1(G)$ such that the generalized Poisson summation formula for $\mu$ holds for all $f\in S_{\mu}(G)$, for all $x\in G$. For the definitions of transformable and translation bounded Radon measures and the generalized Poisson summation formula, we refer to L. Argabright and J. Gil de Lamadrid's monograph in 1974.
Jyunji Inoue,Sin-Ei Takahasi 대한수학회 2019 대한수학회지 Vol.56 No.5
In authors' paper in 2007, it was shown that the BSE-exten\-sion of $C^1_0(\mathbf{R})$, the algebra of continuously differentiable functions $f$ on the real number space $\mathbf{R}$ such that $f$ and $df/dx$ vanish at infinity, is the Lipschitz algebra $Lip_1(\mathbf{R})$. This paper extends this result to the case of $C^n_0(\mathbf{R}^d)$ and $C^{n-1,1}_b(\mathbf{R}^d)$, where $n$ and $d$ represent arbitrary natural numbers. Here $C^n_0(\mathbf{R}^d)$ is the space of all $n$-times continuously differentiable functions $f$ on $\mathbf{R}^d$ whose $k$-times derivatives are vanishing at infinity for $k=0,\ldots,n$, and $C^{n-1,1}_b(\mathbf{R}^d)$ is the space of all $(n-1)$-times continuously differentiable functions on $\mathbf{R}^d$ whose $k$-times derivatives are bounded for $k=0, \ldots ,n-1$, and $(n-1)$-times derivatives are Lipschitz. As a byproduct of our investigation we obtain an important result that $C^{n-1,1}_b(\mathbf{R}^d)$ has a predual.
Essential norms and stability constants of weighted composition
Hiroyuki Takagi,Takeshi Miura,Sin-Ei Takahasi 대한수학회 2003 대한수학회보 Vol.40 No.4
For a weighted composition operator uC_{varphi} on C(X), wedetermine its essential norm and the constant for its Hyers-Ulamstability, in terms of the set varphi ( { x in X : |u(x)| geqr } ) (r > 0).
전라이(Jeon Ra-Ei),전현우(Jeon Hyun-Woo),유용신(Yu Yong-Sin),정인수(Jung In-Su),권춘안(Kwon Choon-An),이찬식(Lee Chansik) 대한건축학회 2011 대한건축학회 학술발표대회 논문집 - 계획계/구조계 Vol.31 No.2(구조계)
The Regulations related Asbestos management were strengthened, while knowing harmful to the human. But it meet the legal requirement. This study extracted 29 asbestos management factors and used IPA Analysis for selecting the factors which need to improve preferentially. As a result, this study confirmed need for improving 13 management factors. This finding will be used as basic data for development of the asbestos management manual.
Inoue, Jyunji,Takahasi, Sin-Ei Korean Mathematical Society 2019 대한수학회지 Vol.56 No.5
In authors' paper in 2007, it was shown that the BSE-extension of $C^1_0(R)$, the algebra of continuously differentiable functions f on the real number space R such that f and df /dx vanish at infinity, is the Lipschitz algebra $Lip_1(R)$. This paper extends this result to the case of $C^n_0(R^d)$ and $C^{n-1,1}_b(R^d)$, where n and d represent arbitrary natural numbers. Here $C^n_0(R^d)$ is the space of all n-times continuously differentiable functions f on $R^d$ whose k-times derivatives are vanishing at infinity for k = 0, ${\cdots}$, n, and $C^{n-1,1}_b(R^d)$ is the space of all (n - 1)-times continuously differentiable functions on $R^d$ whose k-times derivatives are bounded for k = 0, ${\cdots}$, n - 1, and (n - 1)-times derivatives are Lipschitz. As a byproduct of our investigation we obtain an important result that $C^{n-1,1}_b(R^d)$ has a predual.