A version of Hilbert's 13th problem for infinitely differentiable functions

Abstract

In 1957, Kolmogorov and Arnold gave a solution to the 13th problem which had been formulated by Hilbert in 1900. Actually, it is known that there exist many open problems which can be derived from the original problem. From the function-theoretic point of view, Hilbert's 13th problem can be exactly characterized as the superposition representability problem for continuous functions of several variables. In this paper, the solution to the superposition representability problem for infinitely differentiable functions of several variables is given. © 2010 S. Akashi and S. Kodama.