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arXiv · 2409.02623

Chebyshev polynomials related to Jacobi weights

Jacob S. Christiansen·Olof Rubin
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Abstract

We investigate Chebyshev polynomials corresponding to Jacobi weights and determine monotonicity properties of their related Widom factors. This complements work by Bernstein from 1930-31 where the asymptotical behavior of the related Chebyshev norms was established. As a part of the proof, we analyze a Bernstein-type inequality for Jacobi polynomials due to Chow et al. Our findings shed new light on the asymptotical uniform bounds of Jacobi polynomials. We also show a relation between weighted Chebyshev polynomials on the unit circle and Jacobi weighted Chebyshev polynomials on [-1,1]. This generalizes work by Lachance et al. In order to complete the picture we provide numerical experiments on the remaining cases that our proof does not cover.

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Jacob S. Christiansen, Olof Rubin. 2024-09-04. Chebyshev polynomials related to Jacobi weights. https://arxiv.org/abs/2409.02623

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