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Chebyshev polynomials with zeros on the circle and related topics


Authors: L. S. Maergoĭz and N. N. Rybakova
Translated by: S. V. Kislyakov
Original publication: Algebra i Analiz, tom 25 (2013), nomer 6.
Journal: St. Petersburg Math. J. 25 (2014), 965-979
MSC (2010): Primary 41A50
DOI: https://doi.org/10.1090/S1061-0022-2014-01325-8
Published electronically: September 8, 2014
MathSciNet review: 3234841
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

L. S. Maergoĭz
Affiliation: Siberian Federal University, Svobodnyĭ pr. 83, Krasnoyarsk 660041, Russia
Email: bear.lion@mail.ru

N. N. Rybakova
Affiliation: Siberian Federal University, Svobodnyĭ pr. 83, Krasnoyarsk 660041, Russia
Email: ryba-kr@yandex.ru

DOI: https://doi.org/10.1090/S1061-0022-2014-01325-8
Keywords: Polynomial of smallest deviation from zero, Chebyshev alternance
Received by editor(s): March 1, 2012
Published electronically: September 8, 2014
Article copyright: © Copyright 2014 American Mathematical Society