@inbook{89e27b18b67e4771a62e8b41ef049ad4,
title = "Weighted Chebyshev Polynomials on Compact Subsets of the Complex Plane",
abstract = "We study weighted Chebyshev polynomials on compact subsets of the complex plane with respect to a bounded weight function. We establish existence and uniqueness of weighted Chebyshev polynomials and derive weighted analogs of Kolmogorov{\textquoteright}s criterion, the alternation theorem, and a characterization due to Rivlin and Shapiro. We derive invariance of the Widom factors of weighted Chebyshev polynomials under polynomial pre-images and a comparison result for the norms of Chebyshev polynomials corresponding to different weights. Finally, we obtain a lower bound for the Widom factors in terms of the Szeg{\H o} integral of the weight function and discuss its sharpness.",
keywords = "Bernstein–Walsh inequality, Szeg{\H o} lower bound, Weighted Chebyshev polynomials",
author = "Galen Novello and Klaus Schiefermayr and Maxim Zinchenko",
note = "Funding Information: M.Z. was supported in part by Simons Foundation grant CGM–581256. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",
year = "2021",
doi = "10.1007/978-3-030-75425-9\_18",
language = "English",
series = "Operator Theory: Advances and Applications",
publisher = "Springer",
pages = "357--370",
booktitle = "Operator Theory",
address = "Germany",
}