共查询到20条相似文献,搜索用时 15 毫秒
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V. P. Odinets 《Mathematical Notes》1977,22(1):515-517
Suppose that in a normed linear space B there exists a projector with unit norm onto a subspace D. A sufficient condition for this projector to be unique is the existence of a setM D
* which is total on D, each functional in which attains its norm on the unit sphere in D and has a unique extension onto B with preservation of norm. As corollaries to this fact, we obtain a series of sufficient conditions for uniqueness (some of which were previously known) as well as a necessary and sufficient condition for uniqueness.Translated from Matematicheskie Zametki, Vol. 22, No. 1, pp. 45–49, July, 1977.The author thanks M. I. Kadets for useful discussions. 相似文献
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Songxiao Li 《Czechoslovak Mathematical Journal》2007,57(3):1013-1023
This article provided some sufficient or necessary conditions for a class of integral operators to be bounded on mixed norm
spaces in the unit ball.
The author is supported in part by the NNSF China (No. 10671115), grants from Specialized Research Fund for the doctoral program
of Higher Education (No. 20060560002) and NSF of Guangdong Province (No. 06105468). 相似文献
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研究了单位$l_{\infty}$ 范数下边权有界的最小支撑树逆最优值问题。给定一个边赋权无向连通网络$G=(V, E, w)$ , 支撑树$T^0$ , 下界向量$\bm{l}$ , 上界向量$\bm{u}$ 及数值$K$ , 寻求一个新的边权向量$\bm{\bar{w}}$ 满足上下界约束$\bm{l}\le\bar{\bm w}\le {\bm u}$ , 且$T^0$ 是在向量$\bm{\bar{w}}$ 下权值为$K$ 的一个最小支撑树, 目标是在单位$l_{\infty}$ 范数下使得修改成本$\|\bar{\bm w}-{\bm w}\|$ 最小。本文给出了该问题的数学模型, 分析了其最优性条件, 设计了求解该问题的时间复杂度为$O(|V||E|)$ 的强多项式时间算法。 相似文献
9.
研究了单位$l_{\infty}$ 范数下边权有界的最小支撑树逆最优值问题。给定一个边赋权无向连通网络$G=(V, E, w)$ , 支撑树$T^0$ , 下界向量$\bm{l}$ , 上界向量$\bm{u}$ 及数值$K$ , 寻求一个新的边权向量$\bm{\bar{w}}$ 满足上下界约束$\bm{l}\le\bar{\bm w}\le {\bm u}$ , 且$T^0$ 是在向量$\bm{\bar{w}}$ 下权值为$K$ 的一个最小支撑树, 目标是在单位$l_{\infty}$ 范数下使得修改成本$\|\bar{\bm w}-{\bm w}\|$ 最小。本文给出了该问题的数学模型, 分析了其最优性条件, 设计了求解该问题的时间复杂度为$O(|V||E|)$ 的强多项式时间算法。 相似文献
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Let H(B) be the set of all harmonic functions f on the unit ball B of Rn. For 0 < p, q ≤∞ and a normal weight φ, the mixed norm space Hp,q, φ(B) consists of all functions f in H(B) for which the mixed norm p,q, φ < ∞. In this article, we obtain some characterizations in terms of radial, tangential, and partial derivative norms in Hp,q, φ(B). The parallel results for the Bloch-type space are also obtained. As an application, the analogous problems for polyharmonic functions are discussed. 相似文献
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《复变函数与椭圆型方程》2012,57(12):845-850
In this paper, we express the essential norm of a composition operator on Bergman spaces of the unit ball in terms of an asymptotic upper bound of a quantity involving the pull-back measure induced by the inducing map. The result could be generalized to convex domains of finite type and to the weighted situation. 相似文献
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In this paper we study the order of growth of the uniform norm of the hyperinterpolation operator on the unit sphere S
r−1
⊂ Rr. The hyperinterpolation approximation L
n
ƒ, where ƒ ∈ C(S
r
−1), is derived from the exact L
2 orthogonal projection Π ƒ onto the space P
n
r
(S
r
−1) of spherical polynomials of degree n or less, with the Fourier coefficients approximated by a positive weight quadrature rule that integrates exactly all polynomials
of degree ≤ 2n. We extend to arbitrary r the recent r = 3 result of Sloan and Womersley [9], by proving that under an additional “quadrature regularity” assumption on the quadrature
rule, the order of growth of the uniform norm of the hyperinterpolation operator on the unit sphere is O(n
r
/2−1), which is the same as that of the orthogonal projection Πn, and best possible among all linear projections onto P
n
r
(S
r
−1). 相似文献
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Stevo Stević 《Siberian Mathematical Journal》2009,50(6):1098-1105
Let $
\mathbb{B}
$
\mathbb{B}
be the unit ball in ℂ
n
and let H($
\mathbb{B}
$
\mathbb{B}
) be the space of all holomorphic functions on $
\mathbb{B}
$
\mathbb{B}
. We introduce the following integral-type operator on H($
\mathbb{B}
$
\mathbb{B}
):
$
I_\phi ^g (f)(z) = \int\limits_0^1 {\operatorname{Re} f(\phi (tz))g(tz)\frac{{dt}}
{t}} ,z \in \mathbb{B},
$
I_\phi ^g (f)(z) = \int\limits_0^1 {\operatorname{Re} f(\phi (tz))g(tz)\frac{{dt}}
{t}} ,z \in \mathbb{B},
相似文献
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Stevo Stevi? 《Applied mathematics and computation》2010,217(5):1811-6197
We find an asymptotically equivalent expression to the essential norm of differences of weighted composition operators between weighted-type spaces of holomorphic functions on the unit ball in CN. As a consequence we characterize the compactness of these operators. The boundedness of these operators is also characterized. 相似文献
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Science China Mathematics - Let Mt be an isoparametric foliation on the unit sphere (Sn?1(1), gst) with d principal curvatures. Using the spherical coordinates induced by Mt, we construct a... 相似文献
16.
For a nonempty setE of nonnegative integers letH
E
p, q, a
andH
E
p
be the closed linear span of
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