On the weighted Bojanov-Chebyshev problem and the sum of translates method of Fenton

On the weighted Bojanov-Chebyshev problem and the sum of translates method of Fenton

Minimax and maximin problems are investigated for a special class of functions on the interval $[0,1]$. These functions are sums of translates of positive multiples of one kernel function and a very general external field function. Due to our very general setting the minimax, equioscillation and cha...

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Veröffentlicht in:Sbornik. Mathematics 2023, Vol.214 (8), p.1163-1190
Hauptverfasser: Farkas, Balint, Nagy, Bela, Révész, Szilárd György
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Révész, Szilárd György
description Minimax and maximin problems are investigated for a special class of functions on the interval $[0,1]$. These functions are sums of translates of positive multiples of one kernel function and a very general external field function. Due to our very general setting the minimax, equioscillation and characterization results obtained extend those of Bojanov, Fenton, Hardin, Kendall, Saff, Ambrus, Ball and Erdélyi. Moreover, we discover a surprising intertwining phenomenon of interval maxima, which provides new information even in the most classical extremal problem of Chebyshev. Bibliography: 25 titles.
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