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Uspekhi Mat. Nauk, 1967, Volume 22, Issue 1(133), Pages 77–124 (Mi umn5699)  

This article is cited in 19 scientific papers (total in 20 papers)

Linear superpositions of functions

A. G. Vitushkin, G. M. Henkin


Full text: PDF file (4920 kB)
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English version:
Russian Mathematical Surveys, 1967, 22:1, 77–125

Bibliographic databases:

UDC: 517.5
MSC: 26B40, 26E05

Citation: A. G. Vitushkin, G. M. Henkin, “Linear superpositions of functions”, Uspekhi Mat. Nauk, 22:1(133) (1967), 77–124; Russian Math. Surveys, 22:1 (1967), 77–125

Citation in format AMSBIB
\Bibitem{VitHen67}
\by A.~G.~Vitushkin, G.~M.~Henkin
\paper Linear superpositions of functions
\jour Uspekhi Mat. Nauk
\yr 1967
\vol 22
\issue 1(133)
\pages 77--124
\mathnet{http://mi.mathnet.ru/umn5699}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=237729}
\zmath{https://zbmath.org/?q=an:0162.17601}
\transl
\jour Russian Math. Surveys
\yr 1967
\vol 22
\issue 1
\pages 77--125
\crossref{https://doi.org/10.1070/RM1967v022n01ABEH001204}


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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. B. L. Fridman, “An estimate of the dimension of the null spaces of linear superpositions”, Math. USSR-Sb., 11:1 (1970), 101–114  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. J. Sternfeld, “Dimension theory and superpositions of continuous functions”, Isr J Math, 20:3-4 (1975), 300  crossref  mathscinet  zmath
    4. Y. Sternfeld, “Superpositions of continuous functions”, Journal of Approximation Theory, 25:4 (1979), 360  crossref
    5. E. A. Asarin, “On convergence of uniform approximations of continuous functions”, Russian Math. Surveys, 39:3 (1984), 179–193  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. Federico Girosi, Tomaso Poggio, “Representation Properties of Networks: Kolmogorov's Theorem Is Irrelevant”, neural comput, 1:4 (1989), 465  crossref
    7. A. Pinkus, B. Wajnryb, “A problem of approximation using multivariate polynomials”, Russian Math. Surveys, 50:2 (1995), 319–340  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    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. ERICH PETER KLEMENT, LASZLO T. KOCZY, BERNHARD MOSER, “ARE FUZZY SYSTEMS UNIVERSAL APPROXIMATORS?”, International Journal of General Systems, 28:2-3 (1999), 259  crossref
    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. V. K. Beloshapka, V. S. Vladimirov, A. A. Gonchar, E. P. Dolzhenko, N. G. Kruzhilin, V. V. Napalkov, P. V. Paramonov, A. G. Sergeev, P. L. Ul'yanov, E. M. Chirka, “Anatolii Georgievich Vitushkin (on his 70th birthday)”, Russian Math. Surveys, 57:1 (2002), 183–190  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    12. 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
    13. 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
    14. D. V. Alexeev, “Neural network approximation of several variable functions”, J. Math. Sci., 168:1 (2010), 5–13  mathnet  crossref  mathscinet  elib
    15. Aurél Galántai, “Properties and construction of NCP functions”, Comput Optim Appl, 2011  crossref
    16. Marchenkov S.S., “Operatory iterirovaniya na mnozhestve nepreryvnykh funktsii berovskogo prostranstva”, Vestnik Moskovskogo universiteta. Seriya 15: Vychislitelnaya matematika i kibernetika, 4 (2011), 33–37  elib
    17. 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
    18. Goldenbaum M. Boche H. Stanczak S., “Harnessing Interference for Analog Function Computation in Wireless Sensor Networks”, IEEE Trans. Signal Process., 61:20 (2013), 4893–4906  crossref  isi
    19. 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
    20. Gromov M., “Geometric, algebraic, and analytic descendants of Nash isometric embedding theorems”, Bull. Amer. Math. Soc., 54:2 (2017), 173–245  crossref  mathscinet  zmath  isi  scopus
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