论文标题
平滑山脊功能总和的表示问题
A representation problem for smooth sums of ridge functions
论文作者
论文摘要
在本文中，我们证明，如果某个平滑度类的多元函数由$ k $任意举止的山脊函数表示，那么它可以由相同平滑度类别的$ k $ ridge函数和多项式的$ k-1 $ k-1 $ K-1表示表示。这解决了A. Pinkus在他的专着“山脊功能”中提出的问题，直到多个多项式。
In this paper we prove that if a multivariate function of a certain smoothness class is represented by a sum of $k$ arbitrarily behaved ridge functions, then it can be represented by a sum of $k$ ridge functions of the same smoothness class and a polynomial of degree at most $k-1$. This solves the problem posed by A. Pinkus in his monograph "Ridge Functions" up to a multivariate polynomial.
