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Dokl. Akad. Nauk SSSR, 1957, Volume 114, Number 5, Pages 953–956 (Mi dan22050)  

This article is cited in 28 scientific papers (total in 28 papers)

MATHEMATICS

On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition

A. N. Kolmogorov


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Received: 20.06.1957

Citation: A. N. Kolmogorov, “On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition”, Dokl. Akad. Nauk SSSR, 114:5 (1957), 953–956

Citation in format AMSBIB
\Bibitem{Kol57}
\by A.~N.~Kolmogorov
\paper On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition
\jour Dokl. Akad. Nauk SSSR
\yr 1957
\vol 114
\issue 5
\pages 953--956
\mathnet{http://mi.mathnet.ru/dan22050}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=0111809}
\zmath{https://zbmath.org/?q=an:0090.27103}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. G. Vitushkin, G. M. Henkin, “Linear superpositions of functions”, Russian Math. Surveys, 22:1 (1967), 77–125  mathnet  crossref  mathscinet  zmath
    2. B. L. Fridman, “A nowhere dense space of linear superpositions of functions of several variables”, Math. USSR-Izv., 6:4 (1972), 807–837  mathnet  crossref  mathscinet  zmath
    3. F. A. Gadzhiev, “The Kolmogorov–Słupecki theorem for a three-dimensional sphere”, Russian Math. Surveys, 39:5 (1984), 57–61  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Z. G. Sadyhov, “On dense subalgebras of iterative and pre-iterative algebras of continuous functions”, Russian Math. Surveys, 39:6 (1984), 225–226  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. V. V. Pospelov, “On the theory of singular expansion in a tensor product of Hilbert spaces”, Russian Acad. Sci. Sb. Math., 82:2 (1995), 357–364  mathnet  crossref  mathscinet  zmath  isi
    6. A. N. Gorban', “A generalized approximation theorem and an exact representation of polynomials of several variables by superpositions of polynomials of one variable”, Russian Math. (Iz. VUZ), 42:5 (1998), 4–7  mathnet  mathscinet
    7. A. N. Gorban, “Obobschennaya approksimatsionnaya teorema i vychislitelnye vozmozhnosti neironnykh setei”, Sib. zhurn. vychisl. matem., 1:1 (1998), 11–24  mathnet  mathscinet  zmath
    8. S. S. Marchenkov, “On superpositions of continuous functions defined on a Baire space”, Math. Notes, 66:5 (1999), 577–584  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. D. Repovš, A. B. Skopenkov, “New results on embeddings of polyhedra and manifolds in Euclidean spaces”, Russian Math. Surveys, 54:6 (1999), 1149–1196  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. S. S. Marchenkov, “Impossibility of constructing continuous functions of $(n+1)$ variables from functions of $n$ variables by means of certain continuous operators”, Sb. Math., 192:6 (2001), 863–878  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. A. Yu. Golubkov, “Postroenie vneshnikh i vnutrennikh funktsii predstavleniya nepreryvnykh funktsii mnogikh peremennykh superpozitsiei nepreryvnykh funktsii odnogo peremennogo”, Fundament. i prikl. matem., 8:1 (2002), 27–38  mathnet  mathscinet  zmath
    12. S. A. Bogatyi, “Borsuk's Conjecture, Ryshkov Obstruction, Interpolation, Chebyshev Approximation, Transversal Tverberg's Theorem, and Problems”, Proc. Steklov Inst. Math., 239 (2002), 55–73  mathnet  mathscinet  zmath
    13. A. G. Vitushkin, “On Hilbert's thirteenth problem and related questions”, Russian Math. Surveys, 59:1 (2004), 11–25  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    14. Yu. N. Kulchin, I. V. Denisov, A. V. Panov, N. A. Rybalchenko, “Primenenie perseptronov dlya nelineinoi rekonstruktivnoi tomografii”, Probl. upravl., 4 (2006), 59–63  mathnet
    15. F. M. Ablaev, S. G. Ablaeva, “Problema superpozitsii nepreryvnykh funktsii. Kommunikatsionnyi podkhod.”, Uchen. zap. Kazan. gos. un-ta. Ser. Fiz.-matem. nauki, 150, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2008, 5–18  mathnet  zmath
    16. D. V. Alexeev, “Neural network approximation of several variable functions”, J. Math. Sci., 168:1 (2010), 5–13  mathnet  crossref  mathscinet  elib
    17. K. Asai, “Homogeneous partial differential equations for superpositions of indeterminate functions of several variables”, Izv. Math., 73:1 (2009), 31–46  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    18. S. S. Marchenkov, S. I. Krivospitsky, “Superpositions of continuous functions defined on a Baire space”, Problems Inform. Transmission, 45:4 (2009), 393–399  mathnet  crossref  mathscinet  zmath  isi  elib
    19. A. N. Cherepov, “On approximation of continuous functions by determinate functions with delay”, Discrete Math. Appl., 20:1 (2010), 1–24  mathnet  crossref  crossref  mathscinet  zmath  elib
    20. S. S. Marchenkov, “Interpolation and Superpositions of Multivariate Continuous Functions”, Math. Notes, 93:4 (2013), 571–577  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    21. A. I. Vorob'ev, “Characterizing quasiconvex functions in terms of the Kronrod's tree of a function”, Sb. Math., 205:6 (2014), 777–780  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    22. I. I. Slepovichev, “Algebraicheskie svoistva abstraktnykh neironnykh setei”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 16:1 (2016), 96–103  mathnet  crossref  mathscinet  elib
    23. Yu. I. Eremenko, A. I. Gluschenko, “O razrabotke metoda vybora struktury neironnoi seti dlya resheniya zadachi adaptatsii parametrov lineinykh regulyatorov”, UBS, 62 (2016), 75–123  mathnet  elib
    24. V. E. Ismailov, “Approximation by sums of ridge functions with fixed directions”, St. Petersburg Math. J., 28:6 (2017), 741–772  mathnet  crossref  isi  elib
    25. A. I. Ivanov, P. S. Lozhnikov, A. E. Sulavko, “Otsenka nadezhnosti verifikatsii avtografa na osnove iskusstvennykh neironnykh setei, setei mnogomernykh funktsionalov Baiesa i setei kvadratichnykh form”, Kompyuternaya optika, 41:5 (2017), 765–774  mathnet  crossref
    26. A. S. Shvedov, “Approksimatsiya funktsii s pomoschyu neironnykh setei i nechetkikh sistem”, Probl. upravl., 1 (2018), 21–29  mathnet
    27. S. V. Konyagin, A. A. Kuleshov, V. E. Maiorov, “Some problems in the theory of ridge functions”, Proc. Steklov Inst. Math., 301 (2018), 144–169  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    28. N. A. Vershkov, V. A. Kuchukov, N. N. Kuchukova, “Teoreticheskii podkhod k poisku globalnogo ekstremuma pri obuchenii neironnykh setei”, Trudy ISP RAN, 31:2 (2019), 41–52  mathnet  crossref  elib
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