Article Outline
Keywords
See also
References
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arnold V (1957) On the representation of continuous functions of three variables as superpositions of continuous functions of two variables. Dokl Akad Nauk SSSR 114(4):679–681(in Russian.)
Arnold V (1970) On cohomology classes of algebraic functions invariant under a Tschirnhausen transformation. Funkts Anal i Prilozhen 4(1):84–85(in Russian.)
Bari N (1930) Memoire sur la representation finie des fonctions continues. Math Anal 103:185–248
Bassalygo L (1966) On the representation of continuous functions of two variables by continuous functions of one variable. Vestn MGU Ser Mat-Mekh 21:58–63(in Russian).
Chebotarev N (1943) The resolvent problem and critical manifolds. Izv Akad Nauk SSSR Ser Mat 7:123–146(in Russian.)
Chebotarev N (1954) On the resolvent problem. Uchen Zap Kazan Univ 114(2):189–193(in Russian.)
Fridman B (1967) Increasing smoothness of functions in Kolmogorov's theorem on superpositions. Dokl Akad Nauk SSSR 177:1019–1022(in Russian.)
Hilbert D (1902) Sur les problemes futurs des mathematiques. Proc. Second Internat. Congress of Mathematicians, Gauthier-Villars, 58–114
Hilbert D (1927) Ueber die Gleichung neunten Grades. Math Ann 97:243–250
Kantor J (1996) Hilbert's problems and their sequels. Math Intelligencer 18(1):21–30
Kolmogorov A (1956) On the representation of continuous functions of several variables as superpositions of continuous functions of a smaller number of variables. Dokl Akad Nauk SSSR 108(2):179–182 (in Russian.)
Kolmogorov A (1957) On the representation of continuous functions of several variables as superpositions of continuous functions of one variable and addition. Dokl Akad Nauk SSSR 114(5):953–956 (in Russian.)
Korotkich V (1990) Multilevel dichotomy algorithm in global optimization. In: Sebastian H, Tammer K (eds) System Modelling and Optimization. Springer, Berlin, pp 161–169
Kronrod A (1950) Uspekhi Mat Nauk 5(1):24–134(in Russian.)
Lin V (1976) Superpositions of algebraic functions. Funkts Anal i Prilozhen 10(1):37–45(in Russian.)
Lorenz G (1962) Metric entropy, width and superpositions of functions. Amer Math Monthly 69:469–485
Morozov V (1954) On some questions in the resolvent problem. Uchen Zap Kazan Univ 114(2):173–187(in Russian.)
Sprecher D (1965) On the structure of continuous functions of several variables. Trans Amer Math Soc 115:340–355
Sprecher D (1972) An improvement in the superposition theorem of Kolmogorov. J Math Anal Appl 38:208–213
Tikhomirov V (1963) A.N. Kolmogorov's work on ε-entropy of function classes and superpositions of functions. Uspekhi Mat Nauk 18(5):55–92(in Russian.)
Tikhomirov V (ed) (1991) Selected works of A.N. Kolmogorov: Mathematics and mechanics, vol 1. Kluwer, Dordrecht
Traub J, Wasilkowski G, Wozniakowski H (1988) Information-based complexity. Acad. Press, New York
Traub J, Wozniakowski H (1980) Theory of optimal algorithms. Acad. Press, New York
Tschirnhausen W (1683) Methodus auferendi omnes terminos intermedios ex data equatione. Acta Eruditorum
Vitushkin A (1955) On multidimensional variations. Gostekhteorizdar
Wiman A (1927) Ueber die Anwendung der Tschirnhausen Transformation auf die Reduktion algebraischer Gleichungen. Nova Acta R Soc Sci Uppsaliensis extraordin. edit.:3–8
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag
About this entry
Cite this entry
Korotkich, V. (2008). Hilbert’s Thirteenth Problem . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_267
Download citation
DOI: https://doi.org/10.1007/978-0-387-74759-0_267
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-74758-3
Online ISBN: 978-0-387-74759-0
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering