Abstract:
Estimates are gotten for the best approximations in L2(0,2π) of a periodic function by trigonometric polynomials in terms of its m-th continuity modulus or in terms of the continuity modulus of its r-th derivative. The inequality
En−1(f)L2<(Cm2m)−1/2ωm(2π/n;f)L2(f≠const)
is proved, where the constant (Cm2m)−1/2 is unimprovable for the whole space L2(0,2π). Two titles are cited in the bibliography.
Citation:
N. I. Chernykh, “The best approximation of periodic functions by trigonometric polynomials in L2”, Mat. Zametki, 2:5 (1967), 513–522; Math. Notes, 2:5 (1967), 803–808
This publication is cited in the following 76 articles:
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R. A. Lasuriya, “Direct and Inverse Theorems on the Approximation of Functions by Fourier–Laplace Sums in the Spaces S(p,q)(σm−1)”, Math. Notes, 98:4 (2015), 601–612
Citation in format AMSBIB
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