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1.
As is well known that the multivariate spline function plays an important role in both theory and application. The paper [1]—[11] hove studied the multivariate spline functions and obtained a lot of results concerning this topic. Especially in [3], the existance theorem has been shown for the case of n-dim entional spline functions. A. Zeniek [10] and P. Alfeld [11] have established some of results about the tetrahedron partition. In this paper. we will show a kind of cubic C~1—interpolations for any n-simplicial partition in R~n. Of course, some of the subdivisions will be needed.  相似文献   

2.
刘金林 《数学季刊》1996,11(3):24-28
This paper discusses some properties of two classes Vk[α,β] and Rk[α,β ]. Sharp distortion theorem and radius of convexity and starlikeness are obtained. Hadamard product of functions in the classes are also studied.  相似文献   

3.
In[1],the Kothe nuclear sequence spaces are described and in[2]the characte-rization of the semi-nuclear and the barreled locally convex spaces by the boundedvariation of functions respectively.In this paper several kinds of bounded variationof operator-valued functions are studied. Let X and Y are Banach spaces,T(t):[0,1]→L(X,Y)be a operator-valued fun-ction.We called T(t)be uniformly bounded variation,if there exist a constantM>0,such that for any partition △:0=t_0相似文献   

4.
Let φ be a Hausdorff measure function and A be an infinite increasing sequence of positive integers. The Hausdorff-type measure φ - mA associated to φ and A is studied. Let X(t)(t ∈ R^N) be certain Gaussian random fields in R^d. We give the exact Hausdorff measure of the graph set GrX([0, 1]N), and evaluate the exact φ - mA measure of the image and graph set of X(t). A necessary and sufficient condition on the sequence A is given so that the usual Hausdorff measure function for X([0, 1] ^N) and GrX([0, 1]^N) are still the correct measure functions. If the sequence A increases faster, then some smaller measure functions will give positive and finite ( φ A)-Hausdorff measure for X([0, 1]^N) and GrX([0, 1]N).  相似文献   

5.
In this paper, the completeness and minimality properties of some random exponential system in a weighted Banach space of complex functions continuous on the real line for convex nonnegative weight are studied. The results may be viewed as a probabilistic version of Malliavin's classical results.  相似文献   

6.
In this paper we introduce a new kind of Baskakov-Schurer-Szász-Beta operators M_(n,p)~q based on q-integers.We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0,∞].Then we obtain the estimates on the rate of convergence and weighted approximation of operators Mqn,pin terms of modulus of continuity.  相似文献   

7.
8.
We study Jackson's inequality between the best approximation of a function f ∈ L_2(R~3) by entire functions of exponential spherical type and its generalized modulus of continuity.We prove Jackson's inequality with the exact constant and the optimal argument in the modulus of continuity.In particular,Jackson's inequality with the optimal parameters is obtained for classical modulus of continuity of order r and Thue–Morse modulus of continuity of order r ∈ N.These results are based on the solution of the generalized Logan problem for entire functions of exponential type.For it we construct a new quadrature formulas for entire functions of exponential type.  相似文献   

9.
Construction and Dimension Analysis for a Class of Fractal Functions   总被引:3,自引:0,他引:3  
In this paper, we construct a class of nowhere differentiable continuous functions by means of the Cantor series expression of real numbers. The constructed functions include some known nondifferentiable functions, such as Bush type functions. These functions are fractal functions since their graphs are in general fractal sets. Under certain conditions, we investigate the fractal dimensions of the graphs of these functions, compute the precise values of Box and Packing dimensions, and evaluate the Hausdorff dimension. Meanwhile, the Holder continuity of such functions is also discussed.  相似文献   

10.
In this paper, the authors get the characterizations of the integral and Car-leson type measure both associated with the invariant gradient for little a-Bloch functions in the unit ball of Cn. As a consequence, some results of Ouyang C H, Yang W S and Zhao R H in [4] and a result of Yang W S in [10] are extended.  相似文献   

11.
In this paper, we obtain some Gel'fand widths of anisotropic Sobolev periodic classes of smooth functions, and average Gel'fand widths of anisotropic Sobolev classes of smooth functions.  相似文献   

12.
凌博  刘永平 《数学学报》2017,60(3):389-400
我们研究了由仅有实零点的代数多项式导出的微分算子确定的广义Sobolev类利用指数型整函数作为逼近工具的最佳限制逼近问题.利用Fourier变换和周期化等方法,得到在L_2(R)范数下的广义Sobolev光滑函数类的相对平均宽度和最佳限制逼近的精确常数,以及当0是这个代数多项式的一个至多2重的零点时,得到最佳限制逼近在L_1(R)范数和一致范数下的广义Sobolev类的精确到阶的结果.  相似文献   

13.
WIDTHS AND AVERAGE WIDTHS OF SOBOLEV CLASSES   总被引:1,自引:0,他引:1  
This paper concerns the problem of the Kolmogorov n-width, the linear re-width, the Gel'fand n-width and the Bernstein re-width of Sobolev classes of the periodic multivariate functions in the space Lp(Td) and the average Bernstein o-width, average Kolmogorov o-widths, the average linear o-widths of Sobolev classes of the multivariate functions in the space LP(R ), where p = (p1,…,pd), 1 < Pj < ∞o, j = 1,2,…,d, or pj = ∞,j = 1,2,…, d. Their weak asymptotic behaviors are established for the corresponding quantities.  相似文献   

14.
We study the approximation of the integration of multivariate functions in the quantum model of computation. Using a new reduction approach we obtain a lower bound of the n-th minimal query error on anisotropic Sobolev class R(Wpr([0, 1]d)) (r R+d). Then combining this result with our previous one we determine the optimal bound of n-th minimal query error for anisotropic Hblder- Nikolskii class R(H∞r([0,1]d)) and Sobolev class R(W∞r([0,1]d)). The results show that for these two types of classes the quantum algorithms give significant speed up over classical deterministic and randomized algorithms.  相似文献   

15.
临界半线性双调和方程非平凡解的存在性   总被引:12,自引:3,他引:9  
该文借助于没有PS条件的翻山引理,并利用Sobolev嵌入的最佳达到函数,克服了由于Sobolev嵌入失紧性而带来的系列困难.证明了含临界增长的两类观调和方程边值问题非平凡解的存在性.  相似文献   

16.
The paper deals with the theory of space mappings. For a generalization of quasiregular mappings important for the investigation of the Sobolev and other known classes of mappings, we propose a simple condition satisfied by all mappings of this kind and only by these mappings. On the basis of conditions of divergence of the integrals, we establish sufficient conditions for the normality of the families of the analyzed classes of mappings and solve the problem of removing isolated singularities. Some applications of the obtained results to mappings from the Sobolev class are discussed.  相似文献   

17.
For the Sobolev classes W p 1 on a “zero” cusp with a Hölder singularity at the vertex, we consider the question of compactness of the embedding of the traces of Sobolev functions into the Lebesgue classes on the boundary of the cusp.  相似文献   

18.
The article concerns the average onesided widths of the Sobolev and Besov classes and the classes of functions with bounded moduli of smoothness. The weak asymptotic results are obtained for the corresponding quantities.  相似文献   

19.
We prove the metric differentiability and approximate metric differentiability for some broad classes of mappings with values in a metric space, including Sobolev classes. By way of application, we derive some metric analogs of area and coarea formulas.  相似文献   

20.
杨柱元  杨宗文  刘永平 《数学学报》2007,50(5):1177-118
给出了各向异性Sobolev类及各向异性Besov类的平均单边宽度,获得了相应的弱渐近估计.  相似文献   

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