共查询到20条相似文献,搜索用时 15 毫秒
1.
Pal-Andrej Nitsche 《Constructive Approximation》2006,24(1):49-70
We consider best N term approximation using anisotropic tensor product wavelet bases ("sparse grids"). We introduce a tensor
product structure ⊗q on certain quasi-Banach spaces. We prove that the approximation
spaces Aαq(L2) and Aαq(H1) equal tensor products of Besov spaces Bαq(Lq), e.g.,
Aαq(L2([0,1]d)) = Bαq(Lq([0,1])) ⊗q · ⊗q Bαq · ·(Lq([0,1])). Solutions to elliptic partial differential equations on polygonal/polyhedral domains belong to these new scales
of Besov spaces. 相似文献
2.
In recent years there have been various attempts at the
representations of {\mbox multivariate} signals such as images, which
outperform wavelets. As is well known, wavelets are not optimal in
that they do not take full advantage of the geometrical
regularities and singularities of the images. Thus these
approaches have been based on tracing curves of singularities and
applying bandlets, curvelets, ridgelets, etc., or allocating some weights to curves of
singularities like the Mumford–Shah functional and its
modifications. In the latter approach a function is approximated
on subdomains where it is smoother but there is a penalty in the
form of the total length (or other measurement) of the
partitioning curves. We introduce a combined measure of smoothness
of the function in several dimensions by augmenting its smoothness
on subdomains by the smoothness of the partitioning curves.
Also, it is known that classical smoothness spaces fail to
characterize approximation spaces corresponding to multivariate
piecewise polynomial nonlinear approximation. We show how the
proposed notion of smoothness can almost characterize these
spaces. The question whether the characterization proposed in this
work can be further simplified remains open. 相似文献
3.
In this paper, Lorentz space of functions of several variables and Besov's class are considered. We establish an exact approximation order of Besov's class by partial sums of Fourier's series for multiple trigonometric system. 相似文献
4.
Winfried Sickel Frauke Sprengel 《Journal of Computational Analysis and Applications》1999,1(3):263-288
We investigate the order of convergence of periodic interpolation on sparse grids (blending interpolation) in the framework of tensor products of Nikol'skij–Besov spaces. To this end, we make use of the uniformity of the considered tensor norms and provide a unified approach to error estimates for the interpolation of univariate periodic functions from Nikol'skij–Besov spaces. 相似文献
5.
We investigate traces of functions, belonging to a class of functions with dominating mixed smoothness in ℝ3, with respect to planes in oblique position. In comparison with the classical theory for isotropic spaces a few new phenomenona
occur. We shall present two different approaches. One is based on the use of the Fourier transform and restricted to p = 2. The other one is applicable in the general case of Besov-Lizorkin-Triebel spaces and based on atomic decompositions. 相似文献
6.
Vyacheslav S. Rychkov 《Mathematische Nachrichten》2001,224(1):145-180
Characterizations via convolutions with smooth compactly supported kernels and other distinguished properties of the weighted Besov–Lipschitz and Triebel–Lizorkin spaces on ℝn with weights that are locally in Ap but may grow or decrease exponentially at infinity are investigated. Square–function characterizations of the weighted Lp and Hardy spaces with the above class of weights are also obtained. A certain local variant of the Calderón reproducing formula is constructed and widely used in the proofs. 相似文献
7.
The subject is traces of Sobolev spaces with mixed Lebesgue norms on Euclidean space. Specifically, restrictions to the hyperplanes given by x1 = 0 and xn = 0 are applied to functions belonging to quasi‐homogeneous, mixed norm Lizorkin–Triebel spaces ; Sobolev spaces are obtained from these as special cases. Spaces admitting traces in the distribution sense are characterised up to the borderline cases; these are also covered in case x1 = 0. For x1 the trace spaces are proved to be mixed‐norm Lizorkin–Triebel spaces with a specific sum exponent; for xn they are similarly defined Besov spaces. The treatment includes continuous right‐inverses and higher order traces. The results rely on a sequence version of Nikol'skij's inequality, Marschall's inequality for pseudodifferential operators (and Fourier multiplier assertions), as well as dyadic ball criteria. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
8.
Frauke Sprengel 《Numerical Functional Analysis & Optimization》2013,34(1-2):273-293
We present a unified approach to error estimates of periodic interpolation on equidistant, full, and sparse grids for functions from a scale of function spaces which includes L 2-Sobolev spaces, the Wiener algebra and the Korobov spaces. 相似文献
9.
We compare function spaces of dominating mixed smoothness and spaces of best approximation with respect to hyperbolic crosses. 相似文献
10.
Tsukasa Iwabuchi 《Mathematical Methods in the Applied Sciences》2014,37(9):1273-1277
The Cauchy problem for the Keller–Segel system of parabolic elliptic type is considered for initial data in the Besov spaces with p < ∞ , and a sufficient condition is given on the existence and the uniqueness of local solutions. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
11.
The aim of the paper is to characterize the global rate of approximation of derivativesf(l)through corresponding derivatives of linear combinations of Post–Widder operators in an appropriate weightedLp-metric using a weighted Ditzian and Totik modulus of smoothness, and also to characterize derivatives of these operators in Besov spaces of Ditzian–Totik type. 相似文献
12.
Characterization of Smoothness of Multivariate Refinable Functions in Sobolev Spaces 总被引:8,自引:0,他引:8
Rong-Qing Jia 《Transactions of the American Mathematical Society》1999,351(10):4089-4112
Wavelets are generated from refinable functions by using multiresolution analysis. In this paper we investigate the smoothness properties of multivariate refinable functions in Sobolev spaces. We characterize the optimal smoothness of a multivariate refinable function in terms of the spectral radius of the corresponding transition operator restricted to a suitable finite dimensional invariant subspace. Several examples are provided to illustrate the general theory.
13.
《Mathematische Nachrichten》2017,290(13):1939-1970
We are concerned with the study of the Cauchy problem for the Navier–Stokes–Poisson system in the critical regularity framework. In the case of a repulsive potential, we first establish the unique global solvability in any dimension for small perturbations of a linearly stable constant state. Next, under a suitable additional condition involving only the low frequencies of the data and in the L2‐critical framework (for simplicity), we exhibit optimal decay estimates for the constructed global solutions, which are similar to those of the barotropic compressible Navier–Stokes system. Our results rely on new a priori estimates for the linearized Navier–Stokes–Poisson system about a stable constant equilibrium, and on a refined time‐weighted energy functional. 相似文献
14.
In this paper, we apply wavelets to consider local norm function spaces with the Lorentz index. Triebel–Lizorkin–Lorentz spaces are based on the real interpolation of the Triebel–Lizorkin spaces. Triebel–Lizorkin–Morrey spaces are based on local norm of the Triebel–Lizorkin spaces. We give a unified depict of spaces that include these two kinds of spaces. Each index of the five index spaces represents a property of functions. We prove the wavelet characterization of the Triebel–Lizorkin–Lorentz–Morrey spaces and use such characterization to study some basic properties of these spaces. 相似文献
15.
This note studies the well‐posedness of the fractional Navier–Stokes equations in some supercritical Besov spaces as well as in the largest critical spaces for β ∈ (1/2,1). Meanwhile, the well‐posedness for fractional magnetohydrodynamics equations in these Besov spaces is also studied. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
16.
17.
Ali Karaisa 《Mathematical Methods in the Applied Sciences》2016,39(9):2401-2410
In this study, we introduce the Durrmeyer type Jakimoski–Leviatan operators and examine their approximation properties. We study the local approximation properties of these operators. Further, we investigate the convergence of these operators in a weighted space of functions and obtain the approximation properties. Furthermore, we give a Voronovskaja type theorem for the our new operators. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
18.
In this paper, we present a characterization of support functionals and smooth points in , the Musielak–Orlicz space equipped with the Orlicz norm. As a result, criterion for the smoothness of is also obtained. Some expressions involving the norms of functionals in , the topological dual of , are proved for arbitrary Musielak–Orlicz functions. 相似文献
19.
In this article we continue with the study of smooth Gauss–Weierstrass singular integral operators over the real line regarding their simultaneous global smoothness preservation property with respect to the Lp norm, 1≤p≤∞, by involving higher order moduli of smoothness. Also we study their simultaneous approximation to the unit operator with rates involving the modulus of continuity with respect to the uniform norm. The produced Jackson type inequalities are almost sharp containing elegant constants, and they reflect the high order of differentiability of the engaged function. 相似文献
20.
A nonlinear integral operator T of the form (Tf)(s)=∫G K(t, f (σ(s, t))) dμ(t), for sG, is defined and investigated in the measure space (G, Σ, μ), where f and K are vector-valued functions with values in normed linear spaces E and F, respectively. The results are applied to the case of integro-differential operators in generalized Orlicz–Sobolev spaces. There are studied problems of existence, embeddings, and approximation by means of T. 相似文献