共查询到20条相似文献,搜索用时 15 毫秒
1.
Makoto Tsukada 《Journal of Approximation Theory》1984,40(4):301-309
Let X be a reflexive, strictly convex Banach space such that both X and X* have Fréchet differentiable norms, and let {Cn} be a sequence of non-empty closed convex subsets of X. We prove that the sequence of best approximations {p(x ¦ Cn)} of any x ε X converges if and only if lim Cn exists and is not empty. We also discuss measurability of closed convex set valued functions. 相似文献
2.
We establish asymptotic equalities for upper bounds of approximations by Fourier sums and for the best approximations in the
metrics of C and L1 on classes of convolutions of periodic functions that can be regularly extended into a fixed strip of the complex plane. 相似文献
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王香庆 《高校应用数学学报(A辑)》2004,19(4):471-478
在各类Besov空间中建立若干等价关系.文中的定理1是Cohen等人2000年论文中的定理4.2的实质性扩充,定理2将李松1997年论文中的定理7延拓到0
相似文献
7.
For functions of bounded variation in the sense of Hardy, we consider the pointwise convergence of the partial sums of Fourier
series over a given sequence of bounded sets in the space of harmonics. We obtain sufficient conditions for convergence; necessary
and sufficient conditions are obtained for the case in which these sets are convex with respect to each coordinate direction.
The Pringsheim convergence of Fourier series in this problem was established by Hardy.
Translated fromMatematicheskie Zametki, Vol. 61, No. 4, pp. 583–595, April, 1997.
Translated by S. A. Telyakovskii and V. N. Temlyakov 相似文献
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A. I. Rubinshtein 《Mathematical Notes》1992,52(6):1239-1246
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S. S. Volosivets 《Siberian Mathematical Journal》2006,47(2):193-208
We obtain some sufficient conditions for convergence of series of the Fourier coefficients with respect to multiplicative systems for functions of bounded p-fluctuation. In some cases we establish the unimprovability of these conditions. 相似文献
12.
Yu. F. Sereda 《Ukrainian Mathematical Journal》1989,41(5):554-559
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 5, pp. 641–647, May, 1989. 相似文献
13.
Yu. K. Dem'yanovich 《Journal of Mathematical Sciences》1980,13(2):202-215
Questions are considered on the rate of convergence (in some abstract space of functions) of approximations that are the best in another space. Under specific conditions it is shown that the best approximations by local functions in a weighted Sobolev space W
p,B
r
yield almost-best approximation in W
q,B
r
with q[p,+).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 58, pp. 22–37, 1976. 相似文献
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Siberian Mathematical Journal - 相似文献
17.
E. M. Nikishin 《Mathematical Notes》1973,14(1):570-574
In this note we show that the condition $$\sqrt {\sum\nolimits_{n = 1}^\infty {f_n^2 (x)} } \in L_p$$ is sufficient for the set of sums of the rearranged series ∑σ fn to be a closed linear set in Lp. 相似文献
18.
G. V. Radzievskii 《Ukrainian Mathematical Journal》1997,49(6):844-864
We establish upper bounds of the best approximations of elements of a Banach space B by the root vectors of an operator A that acts in B. The corresponding estimates of the best approximations are expressed in terms of a K-functional associated with the operator A. For the operator of differentiation with periodic boundary conditions, these estimates coincide with the classical Jackson inequalities for the best approximations of functions by trigonometric polynomials. In terms of K-functionals, we also prove the abstract Dini-Lipschitz criterion of convergence of partial sums of the decomposition of f from B in the root vectors of the operator A to f 相似文献
19.
L. Eichner 《Numerical Functional Analysis & Optimization》2013,34(5):421-439
We are concerned with the Tschebyscheff and Lp-approximation problem, when the approximating family is the union of solutions of linear differential equations. We prove a strong compactness property and a global existence theorem. Application to generalized exponential approximation is given. 相似文献