Geodesic
Comparison of discrete and uniform norms of polynomials on a segment and a circle arc
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 175-183 
S. I. Kalmykov. Comparison of discrete and uniform norms of polynomials on a segment and a circle arc. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 175-183. http://geodesic.mathdoc.fr/item/ZNSL_2012_404_a9/
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     title = {Comparison of discrete and uniform norms of polynomials on a~segment and a~circle arc},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In the paper inequalities containing discrete and uniform norms of polynomials on an interval and a circle arc are proved. The proofs are based on Bernstein-type inequalities. Obtained inequalities supplement some corresponding results of Rakhmanov, Shekhtman, Sheil-Small, Dubinin.

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[2] T. Sheil-Small, “An inequality for the modulus of a polynomial evaluated at the roots of unity”, Bull. London Math. Soc., 40 (2008), 956–964 | DOI | MR | Zbl

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[7] V. N. Dubinin, “Konformnye otobrazheniya i neravenstva dlya algebraicheskikh polinomov”, Algebra i analiz, 13:5 (2001), 16–43 | MR | Zbl

[8] V. N. Dubinin, S. I. Kalmykov, “O polinomakh s ogranicheniyami na dugakh okruzhnosti”, Zap. nauchn. semin. POMI, 392, 2011, 74–83 | MR