A VERSION OF KOLMOGOROV-ARNOLD REPRESENTATION THEOREM FOR DIFFERENTIABLE FUNCTIONS OF SEVERAL VARIABLES

Authors

  • SATOSHI KODAMA Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science,2641 Yamazaki Noda-city Chiba-prefecture, 278-8510, Japan

Keywords:

Kolmogorov-Arnold Representation, Differentiable Functions

Abstract

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

Additional Files

Published

12/21/2011

Issue

Vol. 2 No. 2 (2011): JNAO

Section

Research Articles

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This work is licensed under aย Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.