On Some Properties of Smooth Sums of Ridge Functions

被引：7
|
作者：
Kuleshov, A. A. [1 ]
机构：
[1] Russian Acad Sci, Steklov Math Inst, Ul Gubkina 8, Moscow 119991, Russia
来源：
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2016年 / 294卷 / 01期
基金：
俄罗斯科学基金会;
关键词：
WEIGHTED SOBOLEV SPACES; FINITE SUMS; INTERPOLATION;
D O I：
10.1134/S0081543816060067
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The following problem is studied: If a finite sum of ridge functions defined on an open subset of R-n 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.
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页码：89 / 94
页数：6
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