  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.
