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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.08449 |
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| _version_ | 1866911102266245120 |
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| author | Novello, Galen Schiefermayr, Klaus Zinchenko, Maxim |
| author_facet | Novello, Galen Schiefermayr, Klaus Zinchenko, Maxim |
| contents | We study weighted Chebyshev polynomials on compact subsets of the complex plane with respect to a bounded weight function. We establish existence and uniqueness of weighted Chebyshev polynomials and derive weighted analogs of Kolmogorov's criterion, the alternation theorem, and a characterization due to Rivlin and Shapiro. We derive invariance of the Widom factors of weighted Chebyshev polynomials under polynomial pre-images and a comparison result for the norms of Chebyshev polynomials corresponding to different weights. Finally, we obtain a lower bound for the Widom factors in terms of the Szegő integral of the weight function and discuss its sharpness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08449 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighted Chebyshev Polynomials on Compact Subsets of the Complex Plane Novello, Galen Schiefermayr, Klaus Zinchenko, Maxim Complex Variables We study weighted Chebyshev polynomials on compact subsets of the complex plane with respect to a bounded weight function. We establish existence and uniqueness of weighted Chebyshev polynomials and derive weighted analogs of Kolmogorov's criterion, the alternation theorem, and a characterization due to Rivlin and Shapiro. We derive invariance of the Widom factors of weighted Chebyshev polynomials under polynomial pre-images and a comparison result for the norms of Chebyshev polynomials corresponding to different weights. Finally, we obtain a lower bound for the Widom factors in terms of the Szegő integral of the weight function and discuss its sharpness. |
| title | Weighted Chebyshev Polynomials on Compact Subsets of the Complex Plane |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2508.08449 |