Chebyshev polynomials with zeros on the circle and related topics

Maergoĭz, L.; Rybakova, N.

doi:10.1090/S1061-0022-2014-01325-8

Chebyshev polynomials with zeros on the circle and related topics
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by L. S. Maergoĭz and N. N. Rybakova
Translated by: S. V. Kislyakov

St. Petersburg Math. J. 25 (2014), 965-979

DOI: https://doi.org/10.1090/S1061-0022-2014-01325-8

Published electronically: September 8, 2014

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Abstract:

A description is given for the Chebyshev monic polynomial $T_n^*$ of degree $n$ with zeros on the circle and with the smallest deviation from zero on an arc. The construction of the extremal trigonometric polynomial of order $n/2$ associated with $T_n^*$ is investigated and dual extremal problems are studied. The results are applied to estimating an optimal error for extrapolation from a finite set in the Wiener class.

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