首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 15 毫秒
1.
, , 3. . . f *, f, , f . , .

Research supported by Hungarian National Foundation for Scientific Research Grant No. 1801.  相似文献   

2.
For functions onS d−1 (the unit sphere inR d) and, in particular, forfL p(S d−1), we define new simple moduli of smoothness. We relate different orders of these moduli, and we also relate these moduli to best approximation by spherical harmonics of order smaller thann. Our new moduli lead to sharper results than those now available for the known moduli onL p(S d−1). Supported by NSERC Grant A4816 of Canada.  相似文献   

3.
F. Cohen raised the following question: Determine or estimate a function F(d) so that if we split the integers into two classes at least one class contains, for infinitely many values of d, an arithmetic progression of difference d and length F(d). We prove F(d) ? (1 + ε) log2d.  相似文献   

4.
In this note we find sufficient conditions for uniqueness of expansion of any two functionsf(z) and g(z) which are analytic in the circle ¦ z ¦ < R (0 < R <∞) in series $$f(z) = \sum\nolimits_{n = 0}^\infty {(a_n f_2 (z) + b_n g_n (z))}$$ and $$g_i (z) = \sum\nolimits_{n = 0}^\infty {a_n \lambda _n f_n (z)} + b_n \mu _n f_n (x)),$$ which are convergent in the compact topology, where (f n {z} n=0 and {g} n=0 are given sequences of functions which are analytic in the same circle while {λ n } n=0 and {μ n } n=0 are fixed sequences of complex numbers. The assertion obtained here complements a previously known result of M. G. Khaplanov and Kh. R. Rakhmatov.  相似文献   

5.
6.
Translated from Matematicheskie Zametki, Vol. 52, No. 5, pp. 132–135, November, 1992.  相似文献   

7.
We establish the global smoothness preservation of a function f by the sequence of linear positive operators. Our estimate is in terms of the second order Ditzian-Totik modulus of smoothness. Application is given to the Bernstein operator.  相似文献   

8.
9.
Summary The purpose of this paper is to present a new approach to smoothness of nonperiodic functions. We consider the space of continuous functions on [−1, 1] as well as the weighted Lp-space and introduce a modulus of smoothness that is based on an algebraic addition ⊕ defined on [−1, 1]. The present paper is mainly concerned with general properties and groundwork, whereas a second paper [4] is devoted to more complex properties, in particular to an equivalent K-functional and to the characterization of best algebraic approximation. Moreover the equivalence with the Butzer-Stens modulus will be shown there.  相似文献   

10.
Let fC(R). We are interested in lower and upper bounds of the integrals
  相似文献   

11.
12.
A relation between Gauss-Lucas Theorem and Laguerre Theorem concerning the zeros of a polynomial in complex domain is discussed.  相似文献   

13.
14.
In this paper we will introduce a hyperbolic kind of modulus on the space of multivariate functions of bounded variation and discuss the fundamental properties of the smoothness spaces induced by it. The results obtained, here, can be used to analyze the approximation properties of so-called hyperbolic Lebesgue-Stieltjes convolution operators.  相似文献   

15.
16.
17.
Let R0 and R be resolvents of the operators (?δ) l and (?δ) l +q acting in L2(Em). We study the problem of the belonging of the operator RP?R 0 p to various symmetrically-normed ideals of the ring of bounded operators. We give applications to the theory of scattering.  相似文献   

18.
In the present note certain fundamental estimates of the constructive theory of functions on the sphere Sn Rn+1, n 1, are sharpened on the basis of the equivalence of the K-functional and the modulus of smoothness of functions. In particular a Bernshtein-type inequality for spherical polynomials is made more precise. The estimates obtained are applied to deduce a membership criterion for the function f Lp(Sn), 1 p , to the space Hr Hr Lp(Sn) depending on the growth of the norm of derivatives of best approximation polynomials of the function f, which is an analog of a result found by S. B. Stechkin related to continuous periodic functions.Translated from Matematicheskie Zametki, Vol. 52, No. 3, pp. 123–129, September, 1992.The author wishes to express his deep gratitude to Academician S. M. Nikol'skii and Professor P. I. Lizorkin for discussion of the results of the present note.  相似文献   

19.
20.
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号