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Dokl. Akad. Nauk SSSR, 1957, Volume 114, Number 4, Pages 679–681 (Mi dan22002)  

This article is cited in 23 scientific papers (total in 24 papers)


On functions of three variables

V. I. Arnol'd

Lomonosov Moscow State University

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Presented: А. Н. Колмогоров
Received: 06.04.1957

Citation: V. I. Arnol'd, “On functions of three variables”, Dokl. Akad. Nauk SSSR, 114:4 (1957), 679–681

Citation in format AMSBIB
\by V.~I.~Arnol'd
\paper On functions of three variables
\jour Dokl. Akad. Nauk SSSR
\yr 1957
\vol 114
\issue 4
\pages 679--681

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    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. V. A. Medvedev, “On the representation of functions as a sum of several compositions”, Math. USSR-Sb., 74:1 (1993), 119–130  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. 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
    4. A. L. Garkavi, V. A. Medvedev, S. Ya. Havinson, “Existence of the best possible uniform approximation of a function of several variables by a sum of functions of fewer variables”, Sb. Math., 187:5 (1996), 623–634  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. V. V. Ryzhikov, “Intertwinings of tensor products, and the stochastic centralizer of dynamical systems”, Sb. Math., 188:2 (1997), 237–263  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. D. V. Anosov, A. A. Bolibrukh, V. A. Vassiliev, A. M. Vershik, A. A. Gonchar, M. L. Gromov, S. M. Gusein-Zade, V. M. Zakalyukin, Yu. S. Ilyashenko, V. V. Kozlov, M. L. Kontsevich, Yu. I. Manin, A. I. Neishtadt, S. P. Novikov, Yu. S. Osipov, M. B. Sevryuk, Ya. G. Sinai, A. N. Tyurin, L. D. Faddeev, B. A. Khesin, A. G. Khovanskii, “Vladimir Igorevich Arnol'd (on his 60th birthday)”, Russian Math. Surveys, 52:5 (1997), 1117–1139  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    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. 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
    9. 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
    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. 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
    12. V. N. Burkov, I. V. Burkova, M. V. Popok, “Metod dikhotomicheskogo programmirovaniya”, UBS, 9 (2004), 57–75  mathnet
    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. V. È. Ismailov, “Methods for computing the least deviation from the sums of functions of one variable”, Siberian Math. J., 47:5 (2006), 883–888  mathnet  crossref  mathscinet  zmath  isi  elib
    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. V. A. Vassiliev, “Topological complexity and Schwarz genus of general real polynomial equation”, Mosc. Math. J., 11:3 (2011), 617–625  mathnet  mathscinet
    20. A. G. Dyakonov, “Criteria for the singularity of a pairwise $l_1$-distance matrix and their generalizations”, Izv. Math., 76:3 (2012), 517–534  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    21. 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
    22. 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
    23. A. S. Shvedov, “Approksimatsiya funktsii s pomoschyu neironnykh setei i nechetkikh sistem”, Probl. upravl., 1 (2018), 21–29  mathnet
    24. 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
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