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

doi:10.4213/sm9714e

Balint Farkas, Bela Nagy, Szilárd György Révész

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

Algebra and Number Theory

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

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