Chebyshev polynomials corresponding to a vanishing weight

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Abstract

We consider weighted Chebyshev polynomials on the unit circle corresponding to a weight of the form (z−1)s where s > 0. For integer values of s this corresponds to prescribing a zero of the polynomial on the boundary. As such, we extend findings of Lachance et al. (1979), to non-integer s. Using this generalisation, we are able to relate Chebyshev polynomials on lemniscates and other, more established, categories of Chebyshev polynomials. An essential part of our proof involves the broadening of the Erdos–Lax inequality to encompass powers of polynomials. We believe that this particular result holds ˝ significance in its own right.
Original languageEnglish
Article number106048
JournalJournal of Approximation Theory
Volume301
DOIs
Publication statusPublished - 2024 May 2

Subject classification (UKÄ)

  • Mathematical Analysis

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