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An integral problem of Konyagin and the \((C,L)\)-constants of Nikol’skiń≠. (English. Russian original) Zbl 1126.41016
Subbotin, Yu. N. (ed.), Function theory. Transl. from the Russian. Moscow: MAIK Nauka/ Interperiodica. Proc. Steklov Inst. Math. 2005, Suppl. 2, S117-S138 (2005); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 11, No. 2, 72-91 (2005).
Summary: An extremal problem concerning functions with small supports posed by Konyagin in connection with number-theoretic applications is considered. It is shown to be related to extremal problems on the best Nikol’skii constants in the inequalities for \(C\)- and \(L\)-norms of trigonometric polynomials and entire functions of exponential type. New estimates for constants in these problems are obtained.
For the entire collection see [Zbl 1116.42001].

MSC:
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A44 Best constants in approximation theory
42A05 Trigonometric polynomials, inequalities, extremal problems
11L03 Trigonometric and exponential sums, general
30D15 Special classes of entire functions of one complex variable and growth estimates
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