共查询到20条相似文献,搜索用时 31 毫秒
1.
Dinh Dung 《Journal of Approximation Theory》2000,102(2):1
In the present paper we investigate optimal continuous algorithms in n-term approximation based on various non-linear n-widths, and n-term approximation by the dictionary V formed from the integer translates of the mixed dyadic scales of the tensor product multivariate de la Vallée Poussin kernel, for the unit ball of Sobolev and Besov spaces of functions with common mixed smoothness. The asymptotic orders of these quantities are given. For each space the asymptotic orders of non-linear n-widths and n-term approximation coincide. Moreover, these asymptotic orders are achieved by a continuous algorithm of n-term approximation by V, which is explicitly constructed. 相似文献
2.
Considering Banach Hardy spaces and weighted Bergman spaces, we find the sharp values of the Bernstein, Kolmogorov, Gelfand, and linear n-widths for the classes of analytic functions on the unit disk whose moduli of continuity of the rth derivatives averaged with weight are majorized by a given function satisfying some constraints.
相似文献3.
Lower bounds are obtained for thegl constants and hence also for the unconditional basis constants of subspaces of finite dimensional Banach spaces. Sharp results
are obtained for subspaces ofl
∞
n
, while in the general case thegl constants of “random large” subspaces are related to the distance of “random large” subspaces to Euclidean spaces. In addition,
a new isometric characterization ofl
∞
n
is given, some new information is obtained concerningp-absolutely summing operators, and it is proved that every Banach space of dimensionn contains a subspace whose projection constant is of ordern
1/2.
The research for this paper was begun while both authors were guests of the Mittag-Leffler Institute.
Supported in part by NSF-MCS 79-03042. 相似文献
4.
Estimates of Kolmogorov n-widths and linear n-widths , (1q∞) of Sobolev's classes , (r>0, 1p∞) on compact two-point homogeneous spaces (CTPHS) are established. For part of (p,q)[1,∞]×[1,∞], sharp orders of or were obtained by Bordin et al. (J. Funct. Anal. 202(2) (2003) 307). In this paper, we obtain the sharp orders of and for all the remaining (p,q). Our proof is based on positive cubature formulas and Marcinkiewicz–Zygmund-type inequalities on CTPHS. 相似文献
5.
Using a variational principle for s-numbers, we obtain estimates for the linear, Gel′fand. and Bernstein n-widths. A simple proof of some results concerned with the exact values of n-widths of diagonal operators is given. We also calculate the exact values at the Bernstein n-widths for the Hardy-Sobolev classes. 相似文献
6.
Kernel-based methods in Numerical Analysis have the advantage of yielding optimal recovery processes in the “native” Hilbert space \(\mathcal {H}\) in which they are reproducing. Continuous kernels on compact domains have an expansion into eigenfunctions that are both L 2-orthonormal and orthogonal in \(\mathcal {H}\) (Mercer expansion). This paper examines the corresponding eigenspaces and proves that they have optimality properties among all other subspaces of \(\mathcal {H}\). These results have strong connections to n-widths in Approximation Theory, and they establish that errors of optimal approximations are closely related to the decay of the eigenvalues. Though the eigenspaces and eigenvalues are not readily available, they can be well approximated using the standard n-dimensional subspaces spanned by translates of the kernel with respect to n nodes or centers. We give error bounds for the numerical approximation of the eigensystem via such subspaces. A series of examples shows that our numerical technique via a greedy point selection strategy allows to calculate the eigensystems with good accuracy. 相似文献
7.
S. B. Vakarchuk 《Ukrainian Mathematical Journal》1996,48(4):601-606
In the spaces E q(Ω), 1 < q < ∞, introduced by Smirnov, we obtain exact order estimates of projective and spectral n-widths of the classes W r E p(Ω) and W r E p(Ω)Ф in the case where p and q are not equal. We also indicate extremal subspaces and operators for the approximative values under consideration. 相似文献
8.
Weakly n-dimensional spaces were first distinguished by Karl Menger. In this note we shall discuss three topics concerning this class of spaces: universal spaces, products, and the sum theorem. We prove that there is a universal space for the class of all weakly n-dimensional spaces, present a simpler proof of Tomaszewski’s result about the dimension of a product of weakly n-dimensional spaces, and show that there is an n-dimensional space which admits a pairwise disjoint countable closed cover by weakly n-dimensional subspaces but is not weakly n-dimensional itself. 相似文献
9.
Weakly n-dimensional spaces were first distinguished by Karl Menger. In this note we shall discuss three topics concerning this class
of spaces: universal spaces, products, and the sum theorem. We prove that there is a universal space for the class of all
weakly n-dimensional spaces, present a simpler proof of Tomaszewski’s result about the dimension of a product of weakly n-dimensional spaces, and show that there is an n-dimensional space which admits a pairwise disjoint countable closed cover by weakly n-dimensional subspaces but is not weakly n-dimensional itself.
(Received 17 August 2000) 相似文献
10.
The asymptotic behavior of the n -widths of multiplier operators from L
p
[0,1] into L
q
[0,1] is studied. General upper and lower bounds for the n -widths in terms of the multipliers are established. Moreover, it is shown that these upper and lower bounds coincide for
some important concrete examples.
August 3, 1994. Date revised: November 15, 1996. 相似文献
11.
First we study several extremal problems on minimax, and prove that they are equivalent. Then we connect this result with the exact values of some approximation characteristics of diagonal operators in different settings, such as the best n-term approximation, the linear average and stochastic n-widths, and the Kolmogorov and linear n-widths. Most of these exact values were known before, but in terms of equivalence of these extremal problems, we present a unified approach to give them a direct proof. 相似文献
12.
Elói Medina Galego 《Results in Mathematics》2007,50(1-2):27-41
Suppose that X and Y are Banach spaces complemented in each other with supplemented subspaces A and B. In 1996, W. T. Gowers solved the Schroeder–Bernstein problem for Banach spaces by showing that X is not necessarily isomorphic to Y. In this paper, we obtain some suitable conditions involving the spaces A and B to yield that X is isomorphic to Y or to provide that at least X
m is isomorphic to Yn
for some m, n ∈ IN*. So we get some decomposition methods in Banach spaces via supplemented subspaces resembling Pełczyński’s decomposition methods.
In order to do this, we introduce several notions of Schroeder–Bernstein Quadruples acting on the spaces X, Y, A and B. Thus, we characterize them by using some Banach spaces recently constructed.
Received: October 4, 2005. 相似文献
13.
We explore subspaces of maximal operator spaces (
submaximal spaces) and give a new characterization of such spaces. We show that the set
of n-dimensional submaximal spaces is closed in the topology of c.b. distance,
but not compact. We also investigate subspaces of MAX(L
) and prove that
any homogeneous Hilbertian subspace of MAX(L
1) is completely isomorphic
to R + C. 相似文献
14.
O. G. Parfenov 《Journal of Mathematical Sciences》1997,85(2):1827-1838
This paper contains generalizations of a well-known theorem of Ismagilov on Kolmogorovn-widths in a Hilbert space for Bernstein and Gelfandn-widths. Some examples are considered. Bibliography: 10 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 217, 1994, pp. 112–129. 相似文献
15.
Maite Fernández-Unzueta 《Israel Journal of Mathematics》2012,188(1):301-322
We study the problem of whether every multilinear form defined on the product of n closed subspaces has an extension defined on the product of the entire Banach spaces. We prove that the property derived
from this condition (the Multilinear Extension Property) is local. We use this to prove that, for a wide variety of Banach
spaces, there exist a product of closed subspaces and a multilinear form defined on it, which has no extension to the product
of the entire spaces. We show that the ℓ
p
spaces, with 1 ≤p ≤ ∞ and p ≠ 2, are among them and, more generally, every Banach space which fails to have type p for some p < 2 or cotype q for some q > 2. 相似文献
16.
We study 1-complemented subspaces of the sequence spaces 1 andc
0. In 1, 1-complemented subspaces of codimensionn are those which can be obtained as intersection ofn 1-complemented hyperplanes. Inc
0, we prove a characterization of 1-complemented subspaces of finite codimension in terms of intersection of hyperplanes.Work prepared under the auspices of GNAFA-CNR (National Council of Research) and Minister of Public Instruction of Italy. 相似文献
17.
Yong-ping Liu Gui-qiao XuDepartment of Mathematics Beijing Normal University Beijing China Department of Mathematics Tianjin Normal Univesity Tianjin . China 《应用数学学报(英文版)》2002,18(4):663-674
The classes of the multivariate functions with bounded moduli on Rd and Td are given and their average σ-widths and non-linear n-widths are discussed. The weak asymptotic behaviors are established for the corresponding quantities. 相似文献
18.
S. B. Vakarchuk 《Mathematical Notes》1999,65(2):153-158
We discuss the best linear approximation methods in the Hardy spaceH
q q≥1, for classes of analytic functions studied by N. Ainulloev; these are generalizations (in a certain sense) of function
sets introduced by L. V. Taikov. The exact values of their linear and Gelfandn-widths are obtained. The exact values of the Kolmogorov and Bernsteinn-widths of classes of analytic (in |z|<1) functions whose boundaryK-functionals are majorized by a prescribed functions are also obtained.
Translated fromMatermaticheskie Zametki, Vol. 65, No. 2, pp. 186–193, February, 1999. 相似文献
19.
Given a field F and integer n≥3, we introduce an invariant sn (F) which is defined by examining the vanishing of subspaces of alternating bilinear forms on 2-dimensional subspaces of vector spaces. This invariant arises when we calculate the largest dimension of a subspace of n?×?n skew-symmetric matrices over F which contains no elements of rank 2. We show how to calculate sn (F) for various families of field F, including finite fields. We also prove the existence of large subgroups of the commutator subgroup of certain p-groups of class 2 which contain no non-identity commutators. 相似文献
20.
We consider n-dimensional real Banach spaces X which are far, in the Banach–Mazur distance, from all complemented subspaces of all Banach lattices. We show that this is related to the volume ratio values of X with respect to ellipsoids and to zonoids. 相似文献