Siberian Mathematical Journal

, Volume 60, Issue 3, pp 412–428 | Cite as

An Exact Inequality of Jackson-Chernykh Type for Spline Approximations of Periodic Functions

  • O. L. VinogradovEmail author


We establish the inequality with exact constant for spline approximations of periodic functions which is similar to the Jackson-Chernykh inequality for approximations by trigonometric polynomials. We study the question of the least step in the obtained inequality.


Jackson inequality exact constant splines 


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  1. 1.
    Chernykh N. I., “On the Jackson inequality in L 2,” Proc. Steklov Inst. Math., vol. 88, 75–78 (1967).Google Scholar
  2. 2.
    Korneichuk N. P., Exact Constants in Approximation Theory [Russian], Nauka, Moscow (1987).Google Scholar
  3. 3.
    Arestov V. V. and Chernykh N. I., “On the L 2-approximation of periodic functions by trigonometric polynomials,” in: Approximation and Function Spaces (Proc. Conf. Gdansk, 1979), North-Holland, Amsterdam, 1981, 25–43.Google Scholar
  4. 4.
    Schoenberg I. J., Cardinal Spline Interpolation, SIAM, Philadelphia (1993).zbMATHGoogle Scholar
  5. 5.
    Golomb M., “Approximation by periodic spline interpolants on uniform meshes,” J. Approx. Theory, vol. 1, 26–65 (1968).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Kamada M., Toriachi K., and Mori R., “Periodic spline orthonormal bases,” J. Approx. Theory, vol. 55, 27–34 (1988).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Vinogradov O. L., “Analog of the Akhiezer-Krein-Favard sums for periodic splines of minimal defect,” J. Math. Sci., vol. 114, no. 5, 1608–1627 (2003).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Yudin V. A., “An extremum problem for distribution functions,” Math. Notes, vol. 63, no. 2, 279–282 (1998).MathSciNetCrossRefGoogle Scholar
  9. 9.
    Logan B. F., “Extremal problems for positive-definite bandlimited functions. II. Eventually negative functions,” SIAM J. Math. Anal., vol. 14, no. 2, 253–257 (1993).MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Ivanov V. I., “Approximation in L p by polynomials in the Walsh system,” Math. USSR-Sb., vol. 62, no. 2, 385–402 (1989).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Babenko A. G., “The exact constant in the Jackson inequality in L 2,” Math. Notes, vol. 39, no. 5, 355–363 (1986).CrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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