Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 287647, 5 pages
doi:10.1155/2010/287647
A version of Hilbert's 13th problem for infinitely differentiable functions
Shigeo Akashi
and Satoshi Kodama
Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda City, Chiba Prefecture 278-8510, Japan
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.