共查询到20条相似文献,搜索用时 0 毫秒
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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
3.
Prof. Kirti K. Oberai 《Mathematische Zeitschrift》1968,103(2):122-128
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S. M. Gomes A. K. Kushpel J. Levesley 《Journal of Fourier Analysis and Applications》2001,7(3):283-295
In this article we consider a simple method of radial quasi-interpolation by polynomials on the unit sphere in ℝ3, and present rates of covergence for this method in Sobolev spaces of square integrable functions. We write the discrete
Fourier series as a quasi-interpolant and hence obtain convergence rates, in the aforementioned Sobolev spaces, for the discrete
Fourier projection. We also discuss some typical practical examples used in the context of spherical wavelets. 相似文献
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Song Wenhua 《分析论及其应用》2002,18(4):20-30
In this paper, we study the contraction linearity for metric projection in Lp spaces. A geometrical property of a subspace Y of Lp is given on which Pr is a contraction projection. 相似文献
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P. Wojtaszczyk 《Constructive Approximation》1997,13(1):1-15
In this paper we consider unconditional bases inL p(T), 1<p<∞,p ≠ 2, consisting of trigonometric polynomials. We give a lower bound for the degree of polynomials in such a basis (Theorem 3.4) and show that this estimate is best possible. This is applied to the Littlewood-Paley-type decompositions. We show that such a decomposition has to contain exponential gaps. We also consider unconditional polynomial bases inH p as bases in Bergman-type spaces and show that they provide explicit isomorphisms between Bergman-type spaces and natural sequences spaces. 相似文献
11.
Guanzhen Zhou 《分析论及其应用》2005,21(3):294-300
The present paper introduces a kind of Nevai-Durrmeyer operators which can be used to approximate functions in Lω^p, spaces with the weight ω(x)=1/√(1-x^2) and the approximate rate is also estimated. 相似文献
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A Sobolev space in several variables in anL
1-type norm is not complemented in its second dual. Hence it is not isomorphic as a Banach space to any complemented subspace
of a Banach lattice.
Both authors were supported in part by the Polish KBN grant 2P03A 036 14. 相似文献
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Michael Sand 《Integral Equations and Operator Theory》1996,26(2):210-221
If is a complex, separable Hilbert space, letL
2 () denote theL
2-space of functions defined on the unit circle and having values in . The bilateral shift onL
2() is the operator (U
f)()=f(). A Hilbert spaceH iscontractively contained in the Hilbert spaceK ifHK and the inclusion mapH–K is a contraction. We describe the structure of those Hilbert spaces, contractively contained inL
2(), that are carried into themselves contractively byU
. We also do this for the subcase of those spaces which are carried into themselves unitarily byU
. 相似文献
17.
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
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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
19.
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
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X. H. Sun 《Acta Mathematica Hungarica》1994,65(3):229-236