Skip to main content
Log in

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. N. Kolmogorov [A. N. Kolmogoroff], “Über die beste Annäherung von Funktionen einer gegebenen Funktionklassen,” Ann. Math.,37, 107–111 (1936).

    Google Scholar 

  2. V. M. Tikhomirov, Certain Questions of Approximation Theory [in Russian], Moscow State Univ. (1976).

  3. V. M. Tikhomirov, “Widths of sets in functional spaces and theory of best approximations,” Usp. Mat. Nauk,15, No. 3(93), 81–120 (1960).

    Google Scholar 

  4. L. V. Taikov, “On the best approximation in the mean of certain classes of analytic functions,”Mat. Zametki,1, No. 2, 155–162 (1967).

    Google Scholar 

  5. Yu. N. Subbotin, “Approximation by ‘spline’ functions and estimates of widths,” Tr. Mat. Inst. Akad. Nauk SSSR,109, 35–60 (1971).

    Google Scholar 

  6. M. G. Krein, “On the theory of best approximation of periodic functions,” Dokl. Akad. Nauk SSSR,18, Nos. 4–5, 245–249 (1938).

    Google Scholar 

  7. V. M. Tikhomirov, “Best methods of approximation and interpolation of differentiable functions in the space C[−1, 1],” Mat. Sb.,80, No. 2, 290–304 (1969).

    Google Scholar 

  8. C. K. Chui and P. W. Smith, “Some nonlinear spline approximation problems related to N-widths,” J. Approx. Theory,13, No. 4, 421–430 (1975).

    Google Scholar 

  9. C. A. Micchelli and A. Pinkus, “The exact asymptotic value for the N-widths of smooth functions in L,” in: Approximation Theory, II, G. G. Lorentz, C. K. Chui, and L. L. Schumaker (eds.), Academic Press, New York (1976), pp. 469–474.

    Google Scholar 

  10. C. A. Micchelli and A. Pinkus, “On n-widths in L,” Trans. Am. Math. Soc.,234, No. 1, 139–174 (1977).

    Google Scholar 

  11. C. A. Micchelli and A. Pinkus, “Total positivity and the exact n-widths of certain sets in L1,” Pac. J. Math.,71, No. 2, 499–515 (1977).

    Google Scholar 

  12. C. A. Micchelli and A. Pinkus, “Some problems in the approximation of functions of two variables and n-widths of integral operators,” J. Approx. Theory,24, No. 1, 51–77 (1978).

    Google Scholar 

  13. V. T. Shevaldin, “On a problem of extremal interpolation,” Mat. Zametki,29, No. 4, 603–622 (1981).

    Google Scholar 

  14. Yu. N. Subbotin, “On the connection between finite differences and the corresponding derivatives,” Tr. Mat. Inst. Akad. Nauk SSSR,78, 24–42 (1965).

    Google Scholar 

  15. A. Sharma and I. Tsimbalario, “Some linear differential operators and generalized differences,” Mat. Zametki,21, No. 2, 161–173 (1977).

    Google Scholar 

  16. V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients and Their Application [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  17. L. L. Schumaker, “Toward a constructive theory of generalized spline functions,” in: Spline Functions (Proc. Inter. Symp., Karlsruhe, Germany, May 20–23, 1975), K. Böhmer, G. Meinardus, and W. Schempp (eds.), Lect. Notes in Math., Vol. 501, Springer-Verlag, Berlin-New York (1976), pp. 265–329.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 33, No. 5, pp. 735–744, May, 1983.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shevaldin, V.T. ℒ-Splines and widths. Mathematical Notes of the Academy of Sciences of the USSR 33, 378–383 (1983). https://doi.org/10.1007/BF01158286

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01158286

Navigation