Asymptotics of Chebyshev polynomials, V. residual polynomials
(2023) In Ramanujan Journal 61(1). p.251-278- Abstract
We study residual polynomials, Rx0,n(e), e⊂ R, x∈ R\ e, which are the degree at most n polynomials with R(x) = 1 that minimize the sup norm on e. New are upper bounds on their norms (that are optimal in some cases) and Szegő–Widom asymptotics under fairly general circumstances. We also discuss several illuminating examples and some results in the complex case such as root asymptotics, a universal lower bound, and a new characterization of sets saturating this lower bound.
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- author
- Christiansen, Jacob S. LU ; Simon, Barry and Zinchenko, Maxim
- organization
- publishing date
- 2023
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Residual polynomials, Szegő–Widom asymptotics, Totik–Widom upper bound
- in
- Ramanujan Journal
- volume
- 61
- issue
- 1
- pages
- 251 - 278
- publisher
- Springer
- external identifiers
-
- scopus:85117170036
- ISSN
- 1382-4090
- DOI
- 10.1007/s11139-021-00500-0
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
- id
- 2d591d0a-b594-4642-90be-dea4fe1ade21
- date added to LUP
- 2021-11-16 18:01:49
- date last changed
- 2023-10-26 14:59:38
@article{2d591d0a-b594-4642-90be-dea4fe1ade21, abstract = {{<p>We study residual polynomials, Rx0,n(e), e⊂ R, x∈ R\ e, which are the degree at most n polynomials with R(x) = 1 that minimize the sup norm on e. New are upper bounds on their norms (that are optimal in some cases) and Szegő–Widom asymptotics under fairly general circumstances. We also discuss several illuminating examples and some results in the complex case such as root asymptotics, a universal lower bound, and a new characterization of sets saturating this lower bound.</p>}}, author = {{Christiansen, Jacob S. and Simon, Barry and Zinchenko, Maxim}}, issn = {{1382-4090}}, keywords = {{Residual polynomials; Szegő–Widom asymptotics; Totik–Widom upper bound}}, language = {{eng}}, number = {{1}}, pages = {{251--278}}, publisher = {{Springer}}, series = {{Ramanujan Journal}}, title = {{Asymptotics of Chebyshev polynomials, V. residual polynomials}}, url = {{http://dx.doi.org/10.1007/s11139-021-00500-0}}, doi = {{10.1007/s11139-021-00500-0}}, volume = {{61}}, year = {{2023}}, }