共查询到20条相似文献,搜索用时 0 毫秒
1.
A. S. Romanyuk 《Ukrainian Mathematical Journal》1992,44(5):596-606
We study classes of periodic functions of several variables with bounded generalized derivative in the metric of the space Lp. We obtain order estimates of deviations of Fourier sums, which are constructed depending on the behavior of functions that define the operator of generalized differentiation. We find estimates of the Kolmogorov widths, which are realized by the Fourier sums that are constructed.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 5, pp. 662–672, May, 1992. 相似文献
2.
3.
4.
In an N-dimensional space, we consider the approximation of classes of translation-invariant periodic functions by a linear operator
whose kernel is the product of two kernels one of which is positive. We establish that the least upper bound of this approximation
does not exceed the sum of properly chosen least upper bounds in m-and ((N − m))-dimensional spaces. We also consider the cases where the inequality obtained turns into the equality.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 1, pp. 12–19, January, 2006. 相似文献
5.
Din' Zung 《Journal of Mathematical Sciences》1986,35(6):2859-2875
The paper deals with imbedding theorems and harmonic approximation for classes of periodic functions of several variables. Necessary and sufficient conditions for imbedding are found for various classes of smooth functions. The paper contains asymptotic estimates for fractional order derivatives of multidimensional Dirichlet and Favard kernels, for Fourier best approximation and for the Kolmogorov diameter of smooth function classes.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 10, pp. 207–226, 1984. 相似文献
6.
A. S. Romanyuk 《Ukrainian Mathematical Journal》1991,43(10):1297-1306
Order estimates are obtained for best approximations by polynomials constructed according to hyperbolic crosses on the classes B
p
r
, of periodic functions of several variables. The order is found of the Kolmogorov width on these classes in the spaces Lq for 1 <p q 2.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 10, pp. 1398–1408, October, 1991. 相似文献
7.
R. V. Tovkach 《Ukrainian Mathematical Journal》2011,62(8):1339-1343
We obtain the exact order of deviations of Fejér sums on the class of continuous functions. This order is determined by a
given majorant of the best approximations. 相似文献
8.
9.
10.
11.
A. S. Romanyuk 《Mathematical Notes》2010,87(3-4):403-415
We obtain order-sharp estimates of best approximations to the classes $B_{p,\theta }^r$ of periodic functions of several variables in the space L q , 1 ≤ p, q ≤ ∞ by trigonometric polynomials with “numbers” of harmonics from step hyperbolic crosses. In the one-dimensional case, we establish the order of deviation of Fourier partial sums of functions from the classes $ B_{1,\theta }^{r_1 } $ in the space L 1. 相似文献
12.
13.
14.
D. B. Bazarkhanov 《Mathematical Notes》1995,57(6):646-648
Translated from Matematicheskie Zametki, Vol. 57, No. 6, pp. 917–919, June, 1995. 相似文献
15.
16.
17.
We obtain exact order estimates for the approximation of the classes B
p,θ
Ω
of periodic functions of many variables in the space L
q
by using operators of orthogonal projection and linear operators satisfying certain conditions.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 5, pp. 692–704, May, 2006. 相似文献
18.
B. I. Golubov 《Mathematical Notes》1975,17(2):108-113
For even N ≥ 2 and δ 2N-3 (for N-2 or 4 we assume that δ > (N-1)/2) we find asymptotic approximations for the quantity $$E_R^\delta (H_{\rm N}^\omega ) = \mathop {sup}\limits_{f \in H_{\rm N}^\omega } \parallel f(x) - S_R^\omega (x,f)\parallel _ \in (R \to \infty ),$$ , where S R δ (x,f) is the spherical Riesz mean of order δ of the Fourier kernel of the functionf(x), and H N ω is the class of periodic functions of N variables whose moduli of continuity do not exceed a given convex modulus of continuity ω(δ). For N 2 and δ > 1/2 the result is known. 相似文献
19.
Yu. Kh. Khasanov 《Russian Mathematics (Iz VUZ)》2010,54(12):72-75
In this paper we study the deviations of periodic functions of two variables from the integral mean values and their Fourier
transforms. In the class of uniform almost periodic functions of two variables we obtain estimates for the deviation from
sums of Marcinkiewicz-Zygmund type. 相似文献