- Results in Nonlinear Analysis
- Vol: 1 Issue: 2
- The existence of polynomials which are unrepresentable in Kolmogorov-Arnold superposition representa...
The existence of polynomials which are unrepresentable in Kolmogorov-Arnold superposition representation
Authors : Shigeo Akashi
Pages : 58-64
View : 10 | Download : 7
Publication Date : 2018-08-31
Article Type : Research
Abstract :In this paper, it is proved that there exist polynomials of three complex variables which cannot be represented as any Kolmogorov-Arnold superposition, which has played important roles in the original version of Hilbert\'s 13th problem.Keywords : Hilbert\'s 13th problem, superposition representation, $\\varepsilon$-entropy