Approximation of the Classes HpΩ of Periodic Functions of Many Variables in the Space Lp

被引：0
作者：
N. V. Derev’yanko
机构：
[1] Ukrainian National Academy of Sciences,Institute of Mathematics
来源：
Ukrainian Mathematical Journal | 2014年 / 66卷
关键词：
Tensor Product; Periodic Function; Trigonometric Polynomial; Sparse Grid; Ukrainian National Academy;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We establish upper estimates for the approximation of the classes HpΩ of periodic functions of many variables by polynomials constructed by using the system obtained as the tensor product of the systems of functions of one variable. These results are then used to establish the exact-order estimates of the orthoprojective widths for the classes HpΩ in the space Lp with p ∈ {1, ∞}.
引用
收藏
页码：707 / 718
页数：11
相关论文
共 24 条
[1]  
Pustovoitov NN(1994)Representation and approximation of periodic functions of many variables with given mixed modulus of continuity Anal. Math. 20 35-48
[2]  
Nikol’skii SM(1963)Functions with dominating mixed derivative satisfying the multiple Hölder condition Sib. Mat. Zh. 4 1342-1364
[3]  
Pustovoitov NN(1999)Approximation of many-dimensional functions with given majorant of mixed moduli of continuity Mat. Zametki 65 107-117
[4]  
Smolyak SA(1963)Quadrature and interpolation formulas for tensor products of some classes of functions Dokl. Akad. Nauk SSSR 148 1042-1045
[5]  
Temlyakov VN(1985)Approximate reconstruction of periodic functions of several variables Mat. Sb. 128 256-268
[6]  
Dung D(1992)Optimal recovery of functions of a certain mixed smoothness J. Math. 20 18-32
[7]  
Andrianov AV(1997)On two methods of generalization of the properties of systems of functions of one variable to their tensor product Tr. Mat. Inst. Ros. Akad. Nauk 219 32-43
[8]  
Temlyakov VN(2007)The Smolyak algorithm, sampling on sparse grids and function spaces of dominating mixed smoothness E. J. Approxim. 13 387-425
[9]  
Sickel W(1989)Spaces of functions of mixed smoothness from the decomposition point of view Tr. Mat. Inst. Akad. Nauk SSSR 187 143-161
[10]  
Ullrich T(2011)Widths and the best approximation of the classes Anal. Math. 37 181-213
123