共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove that forf∈L p , 0<p<1, andk a positive integer, there exists an algebraic polynomialP n of degree ≤n such that $$\left\| {f - P_n } \right\|_p \leqslant C\omega _k^\varphi \left( {f,\frac{1}{n}} \right)_p $$ whereω k ? (f,t)p is the Ditzian-Totik modulus of smoothness off inL p , andC is a constant depending only onk andp. Moreover, iff is nondecreasing andk≤2, then the polynomialP n can also be taken to be nondecreasing. 相似文献
2.
We prove a direct theorem for shape preservingL
p
-approximation, 0p, in terms of the classical modulus of smoothnessw
2(f, t
p
1
). This theorem may be regarded as an extension toL
p
of the well-known pointwise estimates of the Timan type and their shape-preserving variants of R. DeVore, D. Leviatan, and X. M. Yu. It leads to a characterization of monotone and convex functions in Lipschitz classes (and more general Besov spaces) in terms of their approximation by algebraic polynomials.Communicated by Ron DeVore. 相似文献
3.
Yu Xiangming 《数学学报(英文版)》1987,3(4):315-326
We prove that for monotone functionf(x)∈L p [?1, 1], 1≤p<∞, there exists a monotone algebraic polynomialL n (f,x) of degreen such that \(\left\| {f(x) - L_n (f,x)} \right\|_p \leqslant C\omega _{2,\varphi } \left( {f,\frac{1}{n}} \right)_p \) , where \(\varphi (x) = \sqrt {1 - x^2 } \) and ω2,?, is the second-order modulus of smoothness which weighs differently the behavior off(x) in the middle of the interval and near the endpoints. This estimate improves the known result of Shvedov. 相似文献
4.
Letf(x) ∈L p[0,1], 1?p? ∞. We shall say that functionf(x)∈Δk (integerk?1) if for anyh ∈ [0, 1/k] andx ∈ [0,1?kh], we have Δ h k f(x)?0. Denote by ∏ n the space of algebraic polynomials of degree not exceedingn and define $$E_{n,k} (f)_p : = \mathop {\inf }\limits_{\mathop {P_n \in \prod _n }\limits_{P_n^{(\lambda )} \geqslant 0} } \parallel f(x) - P_n (x)\parallel _{L_p [0,1]} .$$ We prove that for any positive integerk, iff(x) ∈ Δ k ∩ L p[0, 1], 1?p?∞, then we have $$E_{n,k} (f)_p \leqslant C\omega _2 \left( {f,\frac{1}{n}} \right)_p ,$$ whereC is a constant only depending onk. 相似文献
5.
G. T. Tachev 《分析论及其应用》1992,8(3):38-50
The purpose of the present paper is to evaluate the error of the approximation of the function f∈L1[0,1] by Kantorovich-Bernstein polynomials in Lp-metric (0<p<1). 相似文献
6.
7.
We investigate Besov spaces and their connection with trigonometric polynomial approximation inL
p[−π,π], algebraic polynomial approximation inL
p[−1,1], algebraic polynomial approximation inL
p(S), and entire function of exponential type approximation inL
p(R), and characterizeK-functionals for certain pairs of function spaces including (L
p[−π,π],B
s
a(L
p[−π,π])), (L
p(R),s
a(Lp(R))),
, and
, where 0<s≤∞, 0<p<1,S is a simple polytope and 0<α<r.
This project is supported by the National Science Foundation of China. 相似文献
8.
It is shown that forL
p, 0p<1, the=">1,>K-functional betweenL
p andW
p
r
is identically zero. Useful measures that are equivalent to the moduli of smoothness are found. The equivalence results that are given are valid for 0p.Communicated by Vilmos Totik. 相似文献
9.
10.
The aim of the present paper is to estimate in a precise manner the integerk=k(p,m,n,∈) so that an arbitrarym-dimensional subspaceX of the spacel
p
n
;p>2, contains an (1+∈)-isomorph ofl
p
k
. The main argument of the proof consists of a probabilistic selection which uses a lemma of Slepian. The same method also
shows that any system of normalized functions inL
p
;p≥2, which is equivalent to the unit vector basis ofl
p
n
, contains, for any∈>0, a subsystem of sizeh proportional ton, which is (1+∈)-equivalent to the unit vector basis ofl
p
h
.
The authors were supported by Grant No. 87-0079 from BSF. 相似文献
11.
12.
Roshdi Khalil 《Annali di Matematica Pura ed Applicata》1990,157(1):245-249
Summary In this note we prove that: if T is a contraction in L(lp) that maps elements of disjoint support to elements of disjoint support, then T is an extreme point of the unit ball of L(lp), 1
i) form a p-orthonormal sequence or the nonzero elements of (yi) form a p-orthonormal sequence for which supp (yi)=N. 相似文献
13.
We show that ifX is the closed linear span inL
p
[0,1] of a subsequence of the Haar system, thenX is isomorphic either tol
p
or toL
p
[0,1], [1<p<∞]. We give criteria to determine which of these cases holds; for a given subsequence, this is independent ofp.
This is part of the second author's Ph.D. dissertation, written at the University of Alberta under the supervision of J. L.
B. Galmen. The first author's research was partially supported by NRC A7552. 相似文献
14.
Werner Linde 《Mathematische Annalen》1986,274(4):617-626
15.
16.
Numerical Algorithms - In this note, the additive block diagonal preconditioner (Bai et al., Numer. Algorithms 62, 655–675 2013) and the block triangular preconditioner (Pearson and Wathen,... 相似文献
17.
An interpretation is given to point interactions of the form −Δ+d inL
p
(ℝ
N
), where Δ is the Laplacian operator andd is a pseudopotential related to the ‘Dirac measure at 0', depending on the dimension. They are described as extensions of
−Δ, defined on the space {u∈C
0
∞
(ℝ
N
)|u(0)=0} that are negative generators of analytic semigroups. This is done forN=1,2 and 1<p<∞ and forN=3 and 3/2<p<3. 相似文献
18.
X. H. Sun 《Acta Mathematica Hungarica》1994,65(3):229-236
19.
Rong-Qing Jia 《Advances in Computational Mathematics》1995,3(4):309-341
Subdivision schemes play an important role in computer graphics and wavelet analysis. In this paper we are mainly concerned
with convergence of subdivision schemes inL
p
spaces (1≤p≤∞). We characterize theL
p
-convergence of a subdivision scheme in terms of thep-norm joint spectral radius of two matrices associated with the corresponding mask. We also discuss various properties of
the limit function of a subdivision scheme, such as stability, linear independence, and smoothness. 相似文献
20.