共查询到20条相似文献,搜索用时 9 毫秒
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This article gives the representations of two types of real functionals on L
∞(Ω, Ƒ) or L
∞(Ω, Ƒ, ℙ) in terms of Choquet integrals. These functionals are comonotonically subadditive and comonotonically convex, respectively. 相似文献
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V. S. Balaganskii 《Proceedings of the Steklov Institute of Mathematics》2009,266(Z1):78-102
In the space L
2 of real-valued measurable 2π-periodic functions that are square summable on the period [0, 2π], the Jackson-Stechkin inequality
$
E_n (f) \leqslant \mathcal{K}_n (\delta ,\omega )\omega (\delta ,f), f \in L^2
$
E_n (f) \leqslant \mathcal{K}_n (\delta ,\omega )\omega (\delta ,f), f \in L^2
相似文献
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José Francisco Rodrigues Manel Sanchón José Miguel Urbano 《Monatshefte für Mathematik》2008,17(1):303-322
The aim of this paper is twofold: to prove, for L
1-data, the existence and uniqueness of an entropy solution to the obstacle problem for nonlinear elliptic equations with variable
growth, and to show some convergence and stability properties of the corresponding coincidence set. The latter follow from
extending the Lewy-Stampacchia inequalities to the general framework of L
1. 相似文献
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K. Hllig 《Journal of Approximation Theory》1981,33(4):318-333
In this paper we complete the investigations started by [14.]. We study C. de Boor's conjecture of the L∞-boundedness of the L2-projection P on smooth splines in the special case of a geometric mesh x = {qv}. A connection to the interpolation projection is established and the uniform boundedness of ¦|P¦|π with respect to q is proved. 相似文献
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Let ƒbe a continuous function and sn be the polynomial of degree at mostn of best L2(μ)-approximation to ƒon [-1,1]. Let Zn(ƒ):=\s{xε[-1,1]:ƒ(x)−sn(x) = 0\s}. Under mild conditions on the measure μ, we prove that Zn(ƒ) is dense in [-1,1]. This answers a question posed independently by A. Kroó and V. Tikhomiroff. It also provides an analogue of the results of Kadec and Tashev (for L∞) and Kroó and Peherstorfer (for L1) for least squares approximation. 相似文献
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Rong-Qing Jia 《Journal of Approximation Theory》1983,37(4):293-310
For an integer k 1 and a geometric mesh (qi)−∞∞ with q ε (0, ∞), let Mi,k(x): = k[qi + k](· − x)+k − 1, Ni,k(x): = (qi + k − qiMi,k(x)/k, and let Ak(q) be the Gram matrix (∝Mi,kNj,k)i,jεz. It is known that Ak(q)−1∞ is bounded independently of q. In this paper it is shown that Ak(q)−1∞ is strictly decreasing for q in [1, ∞). In particular, the sharp upper bound and lower bound for Ak (q)−1 are obtained: for all q ε (0, ∞). 相似文献
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Martin Väth 《Indagationes Mathematicae》1998,9(4):619
The provocative title may be supposed to hold if the axiom of choice is weakened. Even more: The dual space of any Köthe space (real-valued and over a σ-finite measure space) coincides with its associate space in the canonical way; in particular, any Köthe space with Fatou's property is re-flexive. We will show that all this is true in ZF + DC + PMω, where PMω is introduced in the text and holds e.g. in Solovay's model. 相似文献
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System's stability is the most important requirement in control system designs. Fuzzy control system (FCS) should satisfy this requirement also. This paper shows that a linear plant with the formulated Fuzzy Logic Controller (FLC) is a nonlinear system and its stability can be analyzed by applying the Small Gain Theorem or the Circle Criterion. By these two criteria, three FLC design procedures are introduced to guarantee the stabilization of the FCS. Finally, two examples are given to confirm the availability of the proposed design approaches. 相似文献
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Using the maximal function characterization of Hardy spaces,we study the interpolation spaces between H^1 and L^∞on spaces of homogeneous type. 相似文献
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We construct the polynomial pm,n* of degree m which interpolates a given real-valued function f L2[a, b] at pre-assigned n distinct nodes and is the best approximant to f in the L2-sense over all polynomials of degree m with the same interpolatory character. It is shown that the L2-error pm,n* − f → 0 as m → ∞ if f C[a, b]. 相似文献
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Barvinok 《Foundations of Computational Mathematics》2008,2(4):393-412
Abstract. Let G be a compact group acting in a real vector space V . We obtain a number of inequalities relating the L
∞ norm of a matrix element of the representation of G with its L
2k
norm for a positive integer k . As an application, we obtain approximation algorithms to find the maximum absolute value of a given multivariate polynomial
over the unit sphere (in which case G is the orthogonal group) and for the assignment problem of degree d , a hard problem of combinatorial optimization generalizing the quadratic assignment problem (in which case G is the symmetric group). 相似文献
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A square matrix over the complex field with non-negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful permutation representation of G is denoted by p(G). The minimal degree of a faithful representation of G by quasi-permutation matrices over the rational and the complex numbers are denoted by q(G) and c(G) respectively. Finally r(G) denotes the minimal degree of a faithful rational valued complex character of G. In this paper p(G), q(G), c(G) and r(G) are calculated for the groups PSU (3, q2) and SU (3, q2).AMS Subject Classification (2000): 20C15 相似文献
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The automorphism group of the C* -algebra generated by the Toeplitz operatos with symbols being continuous functions on the bicircle is characterized completely.
The investigation is based on the analysis of the behaviour of an automorphism of the Toeplitz algebra on itsC* -ideal chains, and the state of the closed ideals in
. 相似文献
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