Best approximation of periodic functions by trigonometric polynomials in L2 |
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Authors: | N I Chernykh |
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Institution: | (1) Sverdlovsk section of the V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR, USSR |
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Abstract: | Estimates are gotten for the best approximations in L2 (0, 2) 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<(C
2m
m
m(2/n;f)L2(1 const) is proved, where the constant (C
2m
m
)–1/2 is unimprovable for the whole space L2 (0, 2). Two titles are cited in the bibliography.Translated from Matematicheskie Zametki, Vol. 2, No. 5, pp. 513–522, November, 1967. |
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Keywords: | |
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