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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2405.08561 |
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| _version_ | 1866916940934545408 |
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| author | Nikiforova, Tatiana |
| author_facet | Nikiforova, Tatiana |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08561 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimax and maximin problems for sums of translates on the real axis Nikiforova, Tatiana Classical Analysis and ODEs 26A51, 26D07, 49K35 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. |
| title | Minimax and maximin problems for sums of translates on the real axis |
| topic | Classical Analysis and ODEs 26A51, 26D07, 49K35 |
| url | https://arxiv.org/abs/2405.08561 |