The existence of polynomials which are unrepresentable in Kolmogorov-Arnold superposition representation

Yıl 2018, Cilt: 1 Sayı: 2, 58 - 64, 31.08.2018

Shigeo Akashi

https://izlik.org/JA44EW72BM

Öz

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.

Anahtar Kelimeler

Hilbert's 13th problem , superposition representation , $\varepsilon$-entropy

Kaynakça

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• [5] A. N. Kolmogorov, On the representation of continuous functions of several variables by superpositions of continuous functions of one variable and addition, Dokl., 114(1957), 679-681.
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