Best approximations of differentiable functions in the metric of the space L2

  • L. V. Taikov
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Abstract

The relation between the best approximations of periodic functions by trigonometric polynomials and the moduli of continuity of their arbitrary derivatives in the metric of the space L2 is studied.

Keywords

Periodic Function Differentiable Function Trigonometric Polynomial Arbitrary Derivative 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Literature cited

  1. 1.
    A. N. Kolmogorov, “Über die beste Annäherung von Funktionen einer gegebenen Funktionklassen,” Ann. Math.,37, 107–111 (1936).Google Scholar
  2. 2.
    V. M. Tikhomirov, “Diameters of sets in functional spaces and theory of best approximations,” Usp. Mat. Nauk,15, No. 3, 81–120 (1960).Google Scholar
  3. 3.
    N. I. Chernykh, “On the best approximation of periodic functions by trigonometric polynomials in L2,” Mat. Zametki,2, No. 5, 513–522 (1967).Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • L. V. Taikov
    • 1
  1. 1.Moscow Wood Technology InstituteUSSR

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