In this paper, it is proved that there exist polynomials of three complex variables which cannot be represented as any KolmogorovArnold superposition, which has played important roles in the original version of Hilbert's 13th problem.
Primary Language  en 

Journal Section  Articles 
Authors 

Bibtex  @research article { rna429885,
journal = {Results in Nonlinear Analysis},
issn = {},
eissn = {26367556},
address = {Erdal KARAPINAR},
year = {2018},
volume = {1},
pages = {58  64},
doi = {},
title = {The existence of polynomials which are unrepresentable in KolmogorovArnold superposition representation},
key = {cite},
author = {Akashi, Shigeo}
} 
APA  Akashi, S . (2018). The existence of polynomials which are unrepresentable in KolmogorovArnold superposition representation. Results in Nonlinear Analysis, 1 (2), 5864. Retrieved from http://dergipark.org.tr/rna/issue/37067/429885 
MLA  Akashi, S . "The existence of polynomials which are unrepresentable in KolmogorovArnold superposition representation". Results in Nonlinear Analysis 1 (2018): 5864 <http://dergipark.org.tr/rna/issue/37067/429885> 
Chicago  Akashi, S . "The existence of polynomials which are unrepresentable in KolmogorovArnold superposition representation". Results in Nonlinear Analysis 1 (2018): 5864 
RIS  TY  JOUR T1  The existence of polynomials which are unrepresentable in KolmogorovArnold superposition representation AU  Shigeo Akashi Y1  2018 PY  2018 N1  DO  T2  Results in Nonlinear Analysis JF  Journal JO  JOR SP  58 EP  64 VL  1 IS  2 SN  26367556 M3  UR  Y2  2018 ER  
EndNote  %0 Results in Nonlinear Analysis The existence of polynomials which are unrepresentable in KolmogorovArnold superposition representation %A Shigeo Akashi %T The existence of polynomials which are unrepresentable in KolmogorovArnold superposition representation %D 2018 %J Results in Nonlinear Analysis %P 26367556 %V 1 %N 2 %R %U 
ISNAD  Akashi, Shigeo . "The existence of polynomials which are unrepresentable in KolmogorovArnold superposition representation". Results in Nonlinear Analysis 1 / 2 (June 2018): 5864. 