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 50 条
  • [21] ALTERNATING ALGORITHM FOR THE APPROXIMATION BY SUMS OF TWO COMPOSITIONS AND RIDGE FUNCTIONS
    Ismailov, Vugar E.
    PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, 2015, 41 (01): : 146 - 152
  • [22] On the Fractional Sums of Some Special Functions
    Uzun, Banu Unalmis
    RESULTS IN MATHEMATICS, 2019, 74 (01)
  • [23] On the Fractional Sums of Some Special Functions
    Banu Ünalmış Uzun
    Results in Mathematics, 2019, 74
  • [24] Convolution sums of some functions on divisors
    Hahn, Heekyoung
    ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2007, 37 (05) : 1593 - 1622
  • [25] Character sums with exponential functions over smooth numbers
    Banks, William D.
    Friedlander, John B.
    Garaev, Moubariz Z.
    Shparlinski, Igor E.
    INDAGATIONES MATHEMATICAE-NEW SERIES, 2006, 17 (02): : 157 - 168
  • [26] Some Properties of Smooth Convex Functions and Newton's Method
    Denisov, D. V.
    Evtushenko, Yu. G.
    Tret'yakov, A. A.
    DOKLADY MATHEMATICS, 2021, 103 (02) : 76 - 80
  • [27] Some Properties of Smooth Convex Functions and Newton’s Method
    D. V. Denisov
    Yu. G. Evtushenko
    A. A. Tret’yakov
    Doklady Mathematics, 2021, 103 : 76 - 80
  • [28] On some aspects of approximation of ridge functions
    Kolleck, Anton
    Vybiral, Jan
    JOURNAL OF APPROXIMATION THEORY, 2015, 194 : 35 - 61
  • [29] Some Problems in the Theory of Ridge Functions
    S. V. Konyagin
    A. A. Kuleshov
    V. E. Maiorov
    Proceedings of the Steklov Institute of Mathematics, 2018, 301 : 144 - 169
  • [30] Some Problems in the Theory of Ridge Functions
    Konyagin, S., V
    Kuleshov, A. A.
    Maiorov, V. E.
    PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2018, 301 (01) : 144 - 169
12345