Weighted residual polynomials on a circular arc
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915777683128320 |
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| author | Christiansen, Jacob S. Eichinger, Benjamin Rubin, Olof Zinchenko, Maxim |
| author_facet | Christiansen, Jacob S. Eichinger, Benjamin Rubin, Olof Zinchenko, Maxim |
| contents | We study the behavior of weighted residual polynomials on circular arcs, including weighted Chebyshev polynomials. For weights given by reciprocals of polynomials, we establish Szegő-Widom asymptotics. Extending our analysis to less regular weights, we determine the asymptotic behavior of the corresponding weighted Widom factors, generalizing results by Eichinger and Thiran et al. As an application, we derive the asymptotics of Widom factors on certain lemniscatic arcs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05428 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weighted residual polynomials on a circular arc Christiansen, Jacob S. Eichinger, Benjamin Rubin, Olof Zinchenko, Maxim Complex Variables We study the behavior of weighted residual polynomials on circular arcs, including weighted Chebyshev polynomials. For weights given by reciprocals of polynomials, we establish Szegő-Widom asymptotics. Extending our analysis to less regular weights, we determine the asymptotic behavior of the corresponding weighted Widom factors, generalizing results by Eichinger and Thiran et al. As an application, we derive the asymptotics of Widom factors on certain lemniscatic arcs. |
| title | Weighted residual polynomials on a circular arc |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2602.05428 |