Chebyshev polynomials in the complex plane and on the real line
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912912166092800 |
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| author | Rubin, Olof |
| author_facet | Rubin, Olof |
| contents | We present a survey of central developments in the theory of Chebyshev polynomials, introduced by P.~L.~Chebyshev and later extended to the complex plane by G.~Faber. Our primary focus is their defining extremal property: among all polynomials with a prescribed leading coefficient, they minimize the supremum norm on a given compact set. Although we do not present new results, we provide -- in selected cases -- new proofs of known theorems and compile a collection of open problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14175 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chebyshev polynomials in the complex plane and on the real line Rubin, Olof Complex Variables Classical Analysis and ODEs 41A50. 30C10 We present a survey of central developments in the theory of Chebyshev polynomials, introduced by P.~L.~Chebyshev and later extended to the complex plane by G.~Faber. Our primary focus is their defining extremal property: among all polynomials with a prescribed leading coefficient, they minimize the supremum norm on a given compact set. Although we do not present new results, we provide -- in selected cases -- new proofs of known theorems and compile a collection of open problems. |
| title | Chebyshev polynomials in the complex plane and on the real line |
| topic | Complex Variables Classical Analysis and ODEs 41A50. 30C10 |
| url | https://arxiv.org/abs/2411.14175 |