On some properties of smooth sums of ridge functions

被引：0
作者：
A. A. Kuleshov
机构：
[1] Steklov Mathematical Institute of Russian Academy of Sciences,
来源：
Proceedings of the Steklov Institute of Mathematics | 2016年 / 294卷
关键词：
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The following problem is studied: If a finite sum of ridge functions defined on an open subset of Rn belongs to some smoothness class, can one represent this sum as a sum of ridge functions (with the same set of directions) each of which belongs to the same smoothness class as the whole sum? It is shown that when the sum contains m terms and there are m − 1 linearly independent directions among m linearly dependent ones, such a representation exists.
引用
收藏
页码：89 / 94
页数：5
相关论文
共 22 条
  • [1] Aliev R. A.(2016)On a smoothness problem in ridge function representation Adv. Appl. Math. 73 154-169
  • [2] Ismailov V. E.(1993)Interpolation by ridge functions J. Approx. Theory 73 218-236
  • [3] Braess D.(1951)Functions whose differences belong to a given class Nieuw Arch. Wiskd., Ser. 2 23 194-218
  • [4] Pinkus A.(1999)Identifying linear combinations of ridge functions Adv. Appl. Math. 22 103-118
  • [5] de Bruijn N. G.(2015)Additive and multiplicative anisotropic estimates for integral norms of differentiable functions on irregular domains Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 290 293-303
  • [6] Buhmann M. D.(1969)A Chebyshev theorem for the approximation of a function of two variables by sums of the type Izv. Akad. Nauk SSSR, Ser. Mat. 33 650-666
  • [7] Pinkus A.(2013)( J. Approx. Theory 175 91-113
  • [8] Golovko A. Y.(2015)) + Mat. Zametki 98 308-309
  • [9] Havinson S. Y.(2016)( Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 293 193-200
  • [10] Ismailov V. E.(1999)) J. Approx. Theory 99 68-94
123