Skip to main content
SpringerLink
Log in

The octahedron is badly approximated by random subspaces

  • Published:
Functional Analysis and Its Applications Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature Cited

  1. B. S. Kashin, "Diameters of some finite-dimensional sets and classes of smooth functions," Izv. Akad. Nauk SSSR, Ser. Mat.,41, 334–351 (1977).

    Google Scholar 

  2. E. D. Gluskin, "Norms of random matrices and diameters of finite-dimensional sets," Mat. Sb.,120, No. 2, 180–189 (1983).

    Google Scholar 

  3. A. Yu. Garnaev and E. D. Gluskin, "On diameters of the Euclidean ball," Dokl. Akad. Nauk SSSR,277, No. 5, 1048–1052 (1984).

    Google Scholar 

  4. B. S. Kashin, "On diameter of octahedrons," Usp. Mat. Nauk,30, No. 4, 251–252 (1975).

    Google Scholar 

  5. S. B. Stechkin, "On the best approximations of given classes of functions by arbitrary polynomials," Usp. Mat. Nauk,9, No. 1, 133–134 (1954).

    Google Scholar 

  6. M. Z. Solomyak and V. M. Tikhomirov, "On geometric characteristics of the imbedding of the classes W αp in C," Izv. Vyssh. Uchebn. Zaved., Mat.,65, No. 10, 76–81 (1967).

    Google Scholar 

  7. R. S. Ismagilov, "Diameters of sets in linear normed spaces and approximation of functions by trigonometric polynomials," Usp. Mat. Nauk,29, No. 3, 161–178 (1974).

    Google Scholar 

  8. B. S. Kashin, "On the Kolmogorov diameters of octahedra," Dokl. Akad. Nauk SSSR,214, No. 5, 1024–1026 (1979).

    Google Scholar 

  9. K. Höllig, "Approximationzahlen von Sobolev-Einbettungen," Math. Ann.,242, No. 3, 273–281 (1979).

    Google Scholar 

  10. V. N. Sudakov and B. S. Tsirel'son, "Extremal properties of half-spaces for spherically symmetric measures," in: Problems of the Theory of Probability Distributions, J. Sov. Math.,9, No. 1 (1978).

  11. C. Borell, "The Brunn—Minkowski inequality in Gauss space," Invent. Math.,30, No. 2, 207–216 (1975).

    Google Scholar 

  12. T. Figiel, J. Lindenstrauss, and V. D. Milman, "The dimension of almost spherical sections of convex bodies," Acta Math.,139, 53–94 (1977).

    Google Scholar 

  13. E. D. Gluskin, "On estimates from below of the diameters of some finite-dimensional sets," Usp. Mat. Nauk,36, No. 2, 179–180 (1981).

    Google Scholar 

  14. V. I. Levenshtein, "Bounds for packings of metric spaces and some of their applications," Probl. Cybern.,40, 43–110 (1983).

    Google Scholar 

Download references

Authors
  1. E. D. Gluskin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Leningrad Branch of the V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 20, No. 1, pp. 14–20, January–March, 1986.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gluskin, E.D. The octahedron is badly approximated by random subspaces. Funct Anal Its Appl 20, 11–16 (1986). https://doi.org/10.1007/BF01077309

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01077309

Keywords

Search

Navigation