Minimax and maximin problems for sums of translates on the real axis
Classical Analysis and ODEs
2025-09-10 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2405.08561,
title = {Minimax and maximin problems for sums of translates on the real axis},
author = {Tatiana Nikiforova},
journal= {arXiv preprint arXiv:2405.08561},
year = {2025}
}