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Asymptotics of Chebyshev polynomials, V. residual polynomials

Christiansen, Jacob S. and Simon, Barry and Zinchenko, Maxim (2021) Asymptotics of Chebyshev polynomials, V. residual polynomials. Ramanujan Journal . ISSN 1382-4090. doi:10.1007/s11139-021-00500-0. (In Press)

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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 supsup norm on ee. 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.

Item Type:Article
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URLURL TypeDescription ReadCube access Paper
Christiansen, Jacob S.0000-0002-3417-8574
Simon, Barry0000-0003-2561-8539
Zinchenko, Maxim0000-0002-9559-0650
Additional Information:© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021. Received 18 September 2020; Accepted 29 July 2021; Published 18 October 2021. We would like to thank M. Ismail, D. Lubinsky, and K. Schiefermayr for useful comments. 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.
Funding AgencyGrant Number
Swedish Research Council2018-03500
Simons FoundationCGM-581256
Classification Code:Mathematics Subject Classification: 41A50; 30C80; 30C10
Record Number:CaltechAUTHORS:20211129-220847957
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Official Citation:Christiansen, J.S., Simon, B. & Zinchenko, M. Asymptotics of Chebyshev polynomials, V. residual polynomials. Ramanujan J (2021).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112075
Deposited By: Tony Diaz
Deposited On:29 Nov 2021 22:46
Last Modified:29 Nov 2021 22:46

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