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Mathematics of Computation

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The zeros of Faber polynomials
generated by an $m$-star


Author: Arno B. J. Kuijlaars
Journal: Math. Comp. 65 (1996), 151-156
MSC (1991): Primary 30C15; Secondary 65D32
MathSciNet review: 1325869
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Abstract: It is shown that the zeros of the Faber polynomials generated by a regular $m$-star are located on the $m$-star. This proves a recent conjecture of J. Bartolomeo and M. He. The proof uses the connection between zeros of Faber polynomials and Chebyshev quadrature formulas.


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Additional Information

Arno B. J. Kuijlaars
Affiliation: Faculteit Wiskunde en Informatica, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands
Email: arno@fwi.uva.nl

DOI: https://doi.org/10.1090/S0025-5718-96-00684-9
Keywords: Faber polynomials, zero distribution, Chebyshev quadrature
Received by editor(s): June 20, 1994
Additional Notes: Supported by the Netherlands Foundation for Mathematics SMC with financial aid from the Netherlands Organization for the Advancement of Scientific Research NWO
Article copyright: © Copyright 1996 American Mathematical Society