Weighted Chebyshev Polynomials on Compact Subsets of the Complex Plane

Galen Novello, Klaus Schiefermayr, Maxim Zinchenko

    Research output: Chapter in Book/Report/Conference proceedingsChapterpeer-review

    2 Citations (Scopus)

    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’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 Szegő integral of the weight function and discuss its sharpness.

    Original languageEnglish
    Title of host publicationOperator Theory
    Subtitle of host publicationAdvances and Applications
    PublisherSpringer
    Pages357-370
    Number of pages14
    DOIs
    Publication statusPublished - 2021

    Publication series

    NameOperator Theory: Advances and Applications
    Volume285
    ISSN (Print)0255-0156
    ISSN (Electronic)2296-4878

    Keywords

    • Bernstein–Walsh inequality
    • Szegő lower bound
    • Weighted Chebyshev polynomials

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