The paper proves inequalities involving the discrete and uniform norms of polynomials on an interval and a circular arc. The proofs are based on Bernstein type inequalities. The inequalities obtained supplement the corresponding results by Rakhmanov, Shekhtman, Sheil-Small, and Dubinin. Bibliography: 8 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 404, 2012, pp. 175–183.
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Kalmykov, S.I. Comparison of the discrete and uniform norms of polynomials on an interval and a circular arc. J Math Sci 193, 100–105 (2013). https://doi.org/10.1007/s10958-013-1437-z
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DOI: https://doi.org/10.1007/s10958-013-1437-z