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Asymptotics of Chebyshev polynomials, V. residual polynomials

Christiansen, Jacob S. LU ; Simon, Barry and Zinchenko, Maxim (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
; and
organization
publishing date
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}},
}