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Minimax and maximin problems for sums of translates on the real axis. arXiv:2405.08561

Preprint, arXiv:2405.08561 [math.CA] (2024).
Summary: Sums of translates generalize logarithms of weighted algebraic polynomials. The paper presents the solution to the minimax and maximin problems on the real axis for sums of translates. We prove that there is a unique function that is extremal in both problems. The key in our proof is a reduction to the problem on a segment. For this, we work out an analogue of the Mhaskar-Rakhmanov-Saff theorem, too.

MSC:

26A51 Convexity of real functions in one variable, generalizations
26D07 Inequalities involving other types of functions
49K35 Optimality conditions for minimax problems
Full Text: arXiv
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