Asymptotics of Chebyshev polynomials, V. residual polynomials
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1.
Lund University
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2.
California Institute of Technology
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3.
University of New Mexico
Abstract
We study residual polynomials, R^((e))_(x₀,n), e ⊂ ℝ, x₀ ∈ ℝ∖e, which are the degree at most n polynomials with R(x₀) = 1 that minimize the sup 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.
Copyright and License
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023.
Acknowledgement
We would like to thank M. Ismail, D. Lubinsky, and K. Schiefermayr for useful comments.
Funding
J. S. Christiansen: Research supported by VR Grant 2018-03500 from the Swedish Research Council.
B. Simon: Research supported by NSF Grant DMS-1665526.
M. Zinchenko: Research supported in part by Simons Foundation Grant CGM-581256.
Additional details
Identifiers
Related works
- Is new version of
- Discussion Paper: arXiv:2008.09669 (arXiv)
Funding
- Swedish Research Council
- 2018-03500
- NSF
- DMS-1665526
- Simons Foundation
- CGM-581256
Dates
- Submitted
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2020-09-18
- Accepted
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2021-07-29
- Available
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2021-10-18Published
Caltech Custom Metadata
- Caltech groups
- Division of Physics, Mathematics and Astronomy (PMA) , Mathematics Department , Physics Department
- Publication Status
- Published