Geodesic
On uniform approximation of functions by Fourier sums
Sbornik. Mathematics, Tome 42 (1982) no. 4, pp. 515-538

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This paper studies traditional problems on uniform approximation of a continuous $2\pi$-periodic function $f$ by its $n$th Fourier sums $S_n(f)$. To this end the deviation $\|f-S_n(f)\|_{C_{2\pi}}$ is estimated in terms of some new functional characteristics. As an application of the estimates a number of known results (due to Lebesgue, Salem, Stechkin, Ul'yanov, Oskolkov, and others) are obtained. Bibliography: 18 titles. 
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     author = {E. A. Sevast'yanov},
     title = {On uniform approximation of functions by {Fourier} sums},
     journal = {Sbornik. Mathematics},
     pages = {515--538},
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     volume = {42},
     number = {4},
     year = {1982},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1982_42_4_a4/}
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E. A. Sevast'yanov. On uniform approximation of functions by Fourier sums. Sbornik. Mathematics, Tome 42 (1982) no. 4, pp. 515-538. http://geodesic.mathdoc.fr/item/SM_1982_42_4_a4/