Skip to main content
Log in

Chebyshev systems of continuous functions with values in two-dimensional strictly convex normed space

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

Literature cited

  1. A. Haar, “Die Minkowskische Geometrie und die Annäherung an stetige Funktionen,” Math. Ann.,78, 293–311 (1918).

    Google Scholar 

  2. A. N. Kolmogorov, “Note on Chebyshev polynomials deviating least from a given function,” Usp. Mat. Nauk,3, No. 1, 216–221 (1948).

    Google Scholar 

  3. S. I. Zukhovitskii and S. B. Stechkin, “On approximation of abstract functions with values in Banach space,” Dokl. Akad. Nauk SSSR,106, No. 5, 773–776 (1956).

    Google Scholar 

  4. S. I. Zukhovitskii and M. G. Krein, “Note on a possible generalization of Haar and Kolmogorov theorems,” Usp. Mat. Nauk,5, No. 1, 217–229 (1950).

    Google Scholar 

  5. J. C. Mairhuber, “On Haar's theorem concerning Chebyshev approximation problems having unique solutions,” Proc. Am. Math. Soc.,7, No. 4, 609–615 (1956).

    Google Scholar 

  6. É. N. Morozov, “On Chebyshev subspaces of vector-valued functions,” Mat. Zametki,19, No. 3, 347–352 (1976).

    Google Scholar 

  7. I. J. Schoenberg and C. T. Yang, “On the unicity of solutions of problems of best approximation,” Ann. Mat. Pure Appl.,54, 1–12 (1961).

    Google Scholar 

  8. J. M. Overdeck, “On the nonexistence of complex Haar systems,” Bull. Am. Math. Soc.,77, No. 5, 737–740 (1971).

    Google Scholar 

  9. É. N. Morozov, “Note on existence of vector-valued Chebyshev systems,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 4, 117–118 (1978).

    Google Scholar 

  10. V. K. Dzyadyk, Introduction to Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  11. K. Kuratowski, Topology, Academic Press (1969).

  12. P. S. Aleksandrov, Combinatorial Topology [in Russian], GTTI, Moscow (1947).

    Google Scholar 

  13. S. Claytor, “Topological immersions of peanian continua in a spherical surface,” Ann. Math.,35, (2), 809–835 (1935).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 33, No. 3, pp. 365–383, March, 1983.

The author thanks S. B. Stechkin for suggesting the problem and discussion.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Koshcheev, V.A. Chebyshev systems of continuous functions with values in two-dimensional strictly convex normed space. Mathematical Notes of the Academy of Sciences of the USSR 33, 186–195 (1983). https://doi.org/10.1007/BF01686325

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01686325

Keywords

Navigation