A VERSION OF KOLMOGOROV-ARNOLD REPRESENTATION THEOREM FOR DIFFERENTIABLE FUNCTIONS OF SEVERAL VARIABLES - Kodama, S. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2011)
The most revised version of KolmogorovArnoldrepresentation theorem shows that all continuous functions of several variables can be represented as superpositions which are constructed from the sums of continuous functions of one variables. in 2008 Kodama and Akashi show a relation between Kolmogorov-Arnold representation theorem and Vitushkin theorem. In this paper, we discuss the problem asking what kind of differentiable functions of several variables can be represented as KolmogorovArnoldsuperpositions constructed from only several differentiable functions of one variable