Chebyshev polynomials corresponding to a vanishing weight
Bergman, Alex LU and Rubin, Olof 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/f571a270-573c-4478-85a0-30ee243153ec
- author
- Bergman, Alex
LU
and Rubin, Olof
LU
- organization
- publishing date
- 2024-05-02
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Approximation Theory
- volume
- 301
- article number
- 106048
- publisher
- Elsevier
- external identifiers
-
- scopus:85192314230
- ISSN
- 0021-9045
- DOI
- 10.1016/j.jat.2024.106048
- project
- Chebyshev polynomials - Complexities in the complex plane
- language
- English
- LU publication?
- yes
- id
- f571a270-573c-4478-85a0-30ee243153ec
- date added to LUP
- 2024-05-02 15:18:07
- date last changed
- 2024-10-06 11:36:09
@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 > 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 = {{Bergman, Alex and Rubin, Olof}},
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}},
}