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Chebyshev polynomials corresponding to a vanishing weight

Rubin, Olof LU orcid and Bergman, Alex LU (2024) In Journal of Approximation Theory 301.
Abstract
We consider weighted Chebyshev polynomials on the unit circle corresponding to a weight of the
form (z−1)s where s > 0. For integer values of s this corresponds to prescribing a zero of the polynomial
on the boundary. As such, we extend findings of Lachance et al. (1979), to non-integer s. Using this
generalisation, we are able to relate Chebyshev polynomials on lemniscates and other, more established,
categories of Chebyshev polynomials. An essential part of our proof involves the broadening of the
Erdos–Lax inequality to encompass powers of polynomials. We believe that this particular result holds ˝
significance in its own right.
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author
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Contribution to journal
publication status
published
subject
in
Journal of Approximation Theory
volume
301
article number
106048
publisher
Elsevier
ISSN
0021-9045
DOI
10.1016/j.jat.2024.106048
language
English
LU publication?
yes
id
f571a270-573c-4478-85a0-30ee243153ec
date added to LUP
2024-05-02 15:18:07
date last changed
2024-06-05 13:58:03
@article{f571a270-573c-4478-85a0-30ee243153ec,
  abstract     = {{We consider weighted Chebyshev polynomials on the unit circle corresponding to a weight of the<br>
form (z−1)s where s &gt; 0. For integer values of s this corresponds to prescribing a zero of the polynomial<br>
on the boundary. As such, we extend findings of Lachance et al. (1979), to non-integer s. Using this<br>
generalisation, we are able to relate Chebyshev polynomials on lemniscates and other, more established,<br>
categories of Chebyshev polynomials. An essential part of our proof involves the broadening of the<br>
Erdos–Lax inequality to encompass powers of polynomials. We believe that this particular result holds ˝<br>
significance in its own right.}},
  author       = {{Rubin, Olof and Bergman, Alex}},
  issn         = {{0021-9045}},
  language     = {{eng}},
  month        = {{05}},
  publisher    = {{Elsevier}},
  series       = {{Journal of Approximation Theory}},
  title        = {{Chebyshev polynomials corresponding to a vanishing weight}},
  url          = {{http://dx.doi.org/10.1016/j.jat.2024.106048}},
  doi          = {{10.1016/j.jat.2024.106048}},
  volume       = {{301}},
  year         = {{2024}},
}