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Chebyshev Polynomials Related to Jacobi Weights

Christiansen, Jacob S. LU and Rubin, Olof LU orcid (2025) In International Mathematics Research Notices 2025(18).
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 to 1931 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. 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... (More)

We investigate Chebyshev polynomials corresponding to Jacobi weights and determine monotonicity properties of their related Widom factors. This complements work by Bernstein from 1930 to 1931 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. 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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publication status
published
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in
International Mathematics Research Notices
volume
2025
issue
18
article number
rnaf281
publisher
Oxford University Press
external identifiers
  • scopus:105016603042
ISSN
1073-7928
DOI
10.1093/imrn/rnaf281
language
English
LU publication?
yes
id
ab8004af-8c41-4b24-a957-b591a5d9ba6e
date added to LUP
2025-11-28 10:52:52
date last changed
2025-11-28 10:53:58
@article{ab8004af-8c41-4b24-a957-b591a5d9ba6e,
  abstract     = {{<p>We investigate Chebyshev polynomials corresponding to Jacobi weights and determine monotonicity properties of their related Widom factors. This complements work by Bernstein from 1930 to 1931 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. 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.</p>}},
  author       = {{Christiansen, Jacob S. and Rubin, Olof}},
  issn         = {{1073-7928}},
  language     = {{eng}},
  number       = {{18}},
  publisher    = {{Oxford University Press}},
  series       = {{International Mathematics Research Notices}},
  title        = {{Chebyshev Polynomials Related to Jacobi Weights}},
  url          = {{http://dx.doi.org/10.1093/imrn/rnaf281}},
  doi          = {{10.1093/imrn/rnaf281}},
  volume       = {{2025}},
  year         = {{2025}},
}