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

#### Shigeo AKASHİ [1]

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.

Hilbert's 13th problem, superposition representation, $\varepsilon$-entropy
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Primary Language en Articles Author: Shigeo AKASHİ (Primary Author)Institution: Tokyo University of ScienceCountry: Japan Publication Date : August 31, 2018
 Bibtex @research article { rna429885, journal = {Results in Nonlinear Analysis}, issn = {}, eissn = {2636-7556}, address = {}, publisher = {Erdal KARAPINAR}, year = {2018}, volume = {1}, pages = {58 - 64}, doi = {}, title = {The existence of polynomials which are unrepresentable in Kolmogorov-Arnold superposition representation}, key = {cite}, author = {Akashi̇, Shigeo} } APA Akashi̇, S . (2018). The existence of polynomials which are unrepresentable in Kolmogorov-Arnold superposition representation . Results in Nonlinear Analysis , 1 (2) , 58-64 . Retrieved from https://dergipark.org.tr/en/pub/rna/issue/37067/429885 MLA Akashi̇, S . "The existence of polynomials which are unrepresentable in Kolmogorov-Arnold superposition representation" . Results in Nonlinear Analysis 1 (2018 ): 58-64 Chicago Akashi̇, S . "The existence of polynomials which are unrepresentable in Kolmogorov-Arnold superposition representation". Results in Nonlinear Analysis 1 (2018 ): 58-64 RIS TY - JOUR T1 - The existence of polynomials which are unrepresentable in Kolmogorov-Arnold superposition representation AU - Shigeo Akashi̇ Y1 - 2018 PY - 2018 N1 - DO - T2 - Results in Nonlinear Analysis JF - Journal JO - JOR SP - 58 EP - 64 VL - 1 IS - 2 SN - -2636-7556 M3 - UR - Y2 - 2018 ER - EndNote %0 Results in Nonlinear Analysis The existence of polynomials which are unrepresentable in Kolmogorov-Arnold superposition representation %A Shigeo Akashi̇ %T The existence of polynomials which are unrepresentable in Kolmogorov-Arnold superposition representation %D 2018 %J Results in Nonlinear Analysis %P -2636-7556 %V 1 %N 2 %R %U ISNAD Akashi̇, Shigeo . "The existence of polynomials which are unrepresentable in Kolmogorov-Arnold superposition representation". Results in Nonlinear Analysis 1 / 2 (August 2018): 58-64 . AMA Akashi̇ S . The existence of polynomials which are unrepresentable in Kolmogorov-Arnold superposition representation. RNA. 2018; 1(2): 58-64. Vancouver Akashi̇ S . The existence of polynomials which are unrepresentable in Kolmogorov-Arnold superposition representation. Results in Nonlinear Analysis. 2018; 1(2): 58-64.

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