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

2021/12/19 by Bálint Farkas, Farkas, Bálint, Béla Nagy +3 · 1 citation
Mathematics · #41A50 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2112.10169

openalex publication_date 2021/12/19 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

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 obtained minimax, equioscillation, and characterization results extend those of Bojanov, Fenton, Hardin, Kendall, Saff and Ambrus, Ball, Erdélyi. Moreover, we discover a surprising intertwining phenomenon of interval maxima, which provides new information even in the most classical extremal problem of Chebyshev.

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• Homeomorphism theorem for sums of translates on the real axis

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