Geodesic
Exact errors of best approximation for complex-valued periodic functions
Sbornik. Mathematics, Tome 209 (2018) no. 3, pp. 421-431

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We extend Nagy's theorem on best approximation by trigonometric polynomials in the $L_1$ metric to certain complex-valued periodic functions. We use this result to find exact constants of best approximation in $L_1$ and $L_\infty$ on some complex convolution classes. For classes of real-valued convolutions these constants were found by Nikol'skii. As an example, we apply these results to the Schwarz kernel and to the corresponding convolution classes. Bibliography: 20 titles.
Keywords: trigonometric polynomial, complex-valued function, best approximation, Nagy's theorem
Mots-clés : convolution classes. 
@article{SM_2018_209_3_a5,
     author = {M. I. Ganzburg},
     title = {Exact errors of best approximation for complex-valued periodic functions},
     journal = {Sbornik. Mathematics},
     pages = {421--431},
     publisher = {mathdoc},
     volume = {209},
     number = {3},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2018_209_3_a5/}
}
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M. I. Ganzburg. Exact errors of best approximation for complex-valued periodic functions. Sbornik. Mathematics, Tome 209 (2018) no. 3, pp. 421-431. http://geodesic.mathdoc.fr/item/SM_2018_209_3_a5/