On the representability of a continuous multivariate function by sums of ridge functions

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2024-10-09 DOI:10.1016/j.jat.2024.106105

Rashid A. Aliev , Fidan M. Isgandarli

引用次数: 0

Abstract

In this paper, new conditions are found for the representability of a continuous multivariate function as a sum of ridge functions. Using these conditions, we give a new proof for the earlier theorem solving the problem, posed by A.Pinkus in his monograph “Ridge Functions”, up to a multivariate polynomial. That is, we show that if a continuous multivariate function has a representation as a sum of arbitrarily behaved ridge functions, then it can be represented as a sum of continuous ridge functions and some multivariate polynomial.

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论脊函数之和对连续多元函数的可表示性

本文为连续多元函数作为脊函数之和的可表示性找到了新的条件。利用这些条件，我们对 A.Pinkus 在他的专著《脊函数》中提出的解决这一问题的早期定理给出了新的证明，直至多元多项式。也就是说，我们证明了如果一个连续多元函数可以表示为任意表现的脊函数之和，那么它就可以表示为连续脊函数与某个多元多项式之和。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Approximation Theory 数学-数学

CiteScore

1.90

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas. These areas include, among others: • Classical approximation • Abstract approximation • Constructive approximation • Degree of approximation • Fourier expansions • Interpolation of operators • General orthogonal systems • Interpolation and quadratures • Multivariate approximation • Orthogonal polynomials • Padé approximation • Rational approximation • Spline functions of one and several variables • Approximation by radial basis functions in Euclidean spaces, on spheres, and on more general manifolds • Special functions with strong connections to classical harmonic analysis, orthogonal polynomial, and approximation theory (as opposed to combinatorics, number theory, representation theory, generating functions, formal theory, and so forth) • Approximation theoretic aspects of real or complex function theory, function theory, difference or differential equations, function spaces, or harmonic analysis • Wavelet Theory and its applications in signal and image processing, and in differential equations with special emphasis on connections between wavelet theory and elements of approximation theory (such as approximation orders, Besov and Sobolev spaces, and so forth) • Gabor (Weyl-Heisenberg) expansions and sampling theory.