Geodesic
On the Szego --- Taikov inequality for conjugate trigonometric polynomials
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 244-250

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In 1943, Szego found the best constant and all extremal polynomials in the inequality between the uniform norm of a conjugate trigonometric polynomial and the norm of the polynomial with real coefficients. In 1990, Taikov also found the best constant by means of another method. In the present paper, we describe all extremal polynomials with complex coefficients and discuss some properties of the extremal polynomials.
Keywords: trigonometric polynomial, uniform norm, interpolation foumula.
Mots-clés : conjugate polynomial 
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     title = {On the {Szego} --- {Taikov} inequality for conjugate trigonometric polynomials},
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A. O. Serkov. On the Szego --- Taikov inequality for conjugate trigonometric polynomials. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 244-250. http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a21/