Hits:

Indexed by:会议论文

Date of Publication:2007-08-24

Included Journals:EI、CPCI-S、Scopus

Volume:2

Page Number:85-+

Abstract:Ridge functions are multivariate functions of the form g(a center dot x), where g is a univariate function, and a center dot x is the inner product of a is an element of R-d\{0} and x is an element of R-d. We are concerned with the uniqueness of representation of a given function as some sum of ridge functions. We prove that if f (x) = Sigma(m)(i-1)g(i)(a(i)center dot x) = 0 for some ai = (a(1)(i), ... , a(d)(i)) is an element of R-d\{0}, and if g(i) is an element of L-loc(p)(R) (or g(i) is an element of D'(R) and g(i) (a(i)center dot x) is an element of D'(R-d)), then, each g(i) is a polynomial of degree at most m-2. We also prove a theorem on the smoothness of linear combinations of ridge functions. These results improve the existing results.