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1.
The stability is an expected property for functions,which is widely considered in the study of approximation theory and wavelet analysis.In this paper,we consider the Lp,q-stability of the shifts of finitely many functions in mixed Lebesgue spaces L~(p,q)(R~(d+1)).We first show that the shiftsφ(·-k)(k∈Z~(d+1))are Lp,q-stable if and only if for anyξ∈R~(d+1),∑_(k∈Z~(d+1))|φ(ξ+2πk)|~20.Then we give a necessary and sufficient condition for the shifts of finitely many functions in mixed Lebesgue spaces L~(p,q)(R~(d+1))to be Lp,q-stable which improves some known results.  相似文献   

2.
We construct the polynomial pm,n* of degree m which interpolates a given real-valued function f L2[a, b] at pre-assigned n distinct nodes and is the best approximant to f in the L2-sense over all polynomials of degree m with the same interpolatory character. It is shown that the L2-error pm,n*f → 0 as m → ∞ if f C[a, b].  相似文献   

3.
Let X be a 1-connected CW-complex of finite type and Lx its rational homotopy Lie algebra. In this work, we show that there is a spectral sequence whose E2 term is the Lie algebra ExtULx(Q, Lx), and which converges to the homotopy Lie algebra of the classifying space B autX. Moreover, some terms of this spectral sequence are related to derivations of Lx and to the Gottlieb group of X.  相似文献   

4.
We focus on the Lp(R2) theory of the fractional Fourier transform (FRFT) for 1 ≤ p ≤ 2. In L1(R2), we mainly study the properties of the FRFT via introducing the two-parameter chirp operator. In order to get the point-wise convergence for the inverse FRFT, we introduce the fractional convolution and establish the corresponding approximate identities. Then the well-defined inverse FRFT is given via approximation by suitable means, such as fractional Gauss means and Able means. Furthermore, if the signal Fα,βf is received, we give the process of recovering the original signal f with MATLAB. In L2(R2), the general Plancherel theorem, direct sum decomposition, and the general Heisenberg inequality for the FRFT are obtained.  相似文献   

5.
In this paper we pursue the study of the best approximation operator extended from L~Φ to L~φ, where φ denotes the derivative of the function Φ. We get pointwise convergence for the coefficients of the extended best approximation polynomials for a wide class of function f, closely related to the Calder′on–Zygmund class t_m^p(x) which had been introduced in 1961. We also obtain weak and strong type inequalities for a maximal operator related to the extended best polynomial approximation and a norm convergence result for the coefficients is derived. In most of these results, we have to consider Matuszewska–Orlicz indices for the function φ.  相似文献   

6.
In this paper, we prove that suitable weak solution(u, b) of the 3-D MHD equations can be extended beyond T if u∈L~∞(0,T; L~3(R~3)) and the horizontal components b_h of the magnetic field satisfies the well-known Ladyzhenskaya-Prodi-Serrin condition, which improves the corresponding regularity criterion by Mahalov-Nicolaenko-Shilkin.  相似文献   

7.
In a recent paper, D.J. Kleitman and M.E. Saks gave a proof of Huang's conjecture on alphabetic binary trees.

Given a set E = {ei}, I = 0, 1, 2, …, m and assigned positive weights to its elements and supposing the elements are indexed such that w(e0) ≤ w(e1) ≤ … ≤w (em), where w(ei) is the weight of ei, we call the following sequence E* a ‘saw-tooth’ sequence

E*=(e0,em,e1,…,ej,emj,…).

Huang's conjecture is: E* is the most expensive sequence for alphabetic binary trees. This paper shows that this property is true for the L-restricted alphabetic binary trees, where L is the maximum length of the leaves and log2(m + 1) ≤Lm.  相似文献   


8.
As a special case of our main result, we show that for all L> 0, each k-nearest neighbor graph in d dimensions excludes Kh as a depth L minor if h = Ω(Ld). More generally, we prove that the overlap graphs defined by Miller, Teng, Thurston and Vavasis (1993) have this combinatorial property. By a construction of Plotkin, Rao and Smith (1994), our result implies that overlap graphs have “good” cut-covers, answering an open question of Kaklamanis, Krizanc and Rao (1993). Consequently, overlap graphs can be emulated on hypercube graphs with a constant factor of slow-down and on butterfly graphs with a factor of O(log* n) slow-down. Therefore, computations on overlap graphs, such as finite element and finite difference methods on “well-conditioned” meshes and image processing on k-nearest neighbor graphs, can be performed on hypercubic parallel machines with a linear speed-up. Our result, in conjunction with a result of Plotkin, Rao and Smith, also yields a combinatorial proof that overlap graphs have separators of sublinear size. We also show that with high probability, the Delaunay diagram, the relative neighborhood graph, and the k-nearest neighbor graph of a random point set exclude Kh as a depth L minor if h = Ω(Ld/2 log n).  相似文献   

9.
The linear functional equation ∂tz = L(z) − rz is considered. The linear operator L acts on a linear metric space of real functions z depending on t and on a parameter ω belonging to a subset of m. The existence and uniqueness to a nonnegative solution of the initial value problem is shown. An application to a kinetic equation is performed.  相似文献   

10.
Given S1, a starting set of points in the plane, not all on a line, we define a sequence of planar point sets {Si}i=1 as follows. With Si already determined, let Li be the set of all the lines determined by pairs of points from Si, and let Si+1 be the set of all the intersection points of lines in Li. We show that with the exception of some very particular starting configurations, the limiting point set i=1Si is everywhere dense in the plane.  相似文献   

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