Chebyshev polynomials in the complex plane and on the real line

Olof Rubin

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arXiv · 2411.14175

Chebyshev polynomials in the complex plane and on the real line

Olof Rubin

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Abstract

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.

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Olof Rubin. 2024-11-21. Chebyshev polynomials in the complex plane and on the real line. https://arxiv.org/abs/2411.14175

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