Mathematical Notes

, Volume 55, Issue 4, pp 406–412 | Cite as

On interpolation properties of exterior functions in Kolmogorov superpositions

  • S. Ja. Khavinson


Interpolation Property Exterior Function 
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Literature cited

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    A. I. Kolmogorov, “On representation of continuous functions of several variables in the form of superposition of continuous functions of one variable and sum,”Dokl. Akad. Nauk SSSR,108, No. 2, 179–182 (1956).Google Scholar
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    G. G. Lorentz, “Metric entropy widths and superpositions of functions.”Am. Math. Monthly,69, 469–485 (1962).Google Scholar
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    D. Sprecher, “On the structure of representations of continuous functions of several variables as finite sums of continuous functions of one variable,”Proc. Amer. Math. Soc.,17, No. 1, 98–105 (1966).Google Scholar
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    T. Hedberg, “The Kolmogorov superposition theorem. Appendix II,” In: H. S. Shapiro,Topics in Approximation Theory. Lect. Notes in Math., Vol. 187 (1971).Google Scholar
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    J. P. Kahane, “Sur le Theoreme de superposition de Kolmogorov,”J. Appr. Theory,13, 229–234 (1975).CrossRefGoogle Scholar
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    S. A. Vinogradov and V. P. Khavin, “Free interpolation inH and some other classes of functions,”Zap. Nauchn. Sem., Leningrad Otdel. Mat. Inst. Steklova (LOMI),47, 15–54 (1974).Google Scholar
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    K. Gofman,Banach Spaces of Analytical Functions, Nauka, Moscow (1966).Google Scholar
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    A. G. Vitushkin, “On representation of functions by means of superposition and related topics,”Enseign. Math.,23, No. 3–4, 255–320 (1977).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • S. Ja. Khavinson
    • 1
  1. 1.Moscow State Civil Engineering UniversityUSSR

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