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The Turán-type inequalities for complex polynomials in \(L_{0}\)-metrics. (English. Russian original) Zbl 1158.41303
Russ. Math. 52, No. 5, 88-94 (2008); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2008, No. 5, 101-108 (2008).
Summary: We obtain inequalities for measures of trigonometric polynomials of power \((P_n (e^{i\varphi} ))\) and general \((T_n (t))\) types with the help of measures and their \(m\)th derivatives.
41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)
30C10 Polynomials and rational functions of one complex variable
Full Text: DOI
[1] P. Turan, ”Über die Ableitung von Polynomen,” Composito Math. Soc. 7, 89–95 (1939). · JFM 65.0324.01
[2] N. P. Korneichuk, V. F. Babenko, and A. A. Ligun, Extremal Properties of Polynomials and Splines (Naukova Dumka, Kiev, 1992) [in Russian]. · Zbl 0976.41008
[3] G. Pólya and G. Szegö, Problems and Theorem in Analysis, Vol. II (Springer-Verlag, Berlin, New York, 1925; Nauka, Moscow, 1978).
[4] V. V. Arestov, ”Integral Inequalities for Algebraic Polynomials on the Unit Circumference,” Matem. Zametki 48(4), 7–18 (1990). · Zbl 0713.30006
[5] E. A. Storozhenko, ”A Problem of Mahler on the Zeros of a Polynomial and its Derivative,” Matem. Sborn. 187(5), 111–120 (1996). · Zbl 0871.30036 · doi:10.1070/SM1996v187n01ABEH000103
[6] G. Pólya and G. Szegö, Problems and Theorem in Analysis, Vol. I (Springer-Verlag, Berlin, New York, 1925; Nauka, Moscow, 1978).
[7] P. Borwein and T. Erdelyi, Polynomials and Polynomial Inequalities (Springer-Verlag, New York, 1995).
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