Abstract:
In this paper, we obtain inequalities for trigonometric and algebraic polynomials supplementing and strengthening the classical results going back to papers of S. N. Bernstein and I. I. Privalov. The method of proof is based on the construction of the conformal and univalent mapping from a given trigonometric polynomial and on the application of results of the geometric theory of functions of a complex variable to this mapping.
Citation:
A. V. Olesov, “Application of Conformal Mappings to Inequalities for Trigonometric Polynomials”, Mat. Zametki, 76:3 (2004), 396–408; Math. Notes, 76:3 (2004), 368–378
This publication is cited in the following 8 articles:
A. V. Olesov, “Inequalities for majorizing analytic functions and their applications to rational trigonometric functions and polynomials”, Sb. Math., 205:10 (2014), 1413–1441
Nagy B., Totik V., “Bernstein's Inequality for Algebraic Polynomials on Circular Arcs”, Constr. Approx., 37:2 (2013), 223–232
S. I. Kalmykov, “On polynomials and rational functions normalized on the circular arcs”, J. Math. Sci. (N. Y.), 200:5 (2014), 577–585
L. S. Maergoiz, N. N. Rybakova, “Chebyshev polynomials with zeros on a circle and adjacent problems”, St. Petersburg Math. J., 25:6 (2014), 965–979
V. N. Dubinin, “Methods of geometric function theory in classical and modern problems for polynomials”, Russian Math. Surveys, 67:4 (2012), 599–684
V. N. Dubinin, S. I. Kalmukov, “On polynomials with constraints on circular arcs”, J. Math. Sci. (N. Y.), 184:6 (2012), 703–708
V. N. Dubinin, D. B. Karp, V. A. Shlyk, “Izbrannye zadachi geometricheskoi teorii funktsii i teorii potentsiala”, Dalnevost. matem. zhurn., 8:1 (2008), 46–95
V. N. Dubinin, “Schwarz's lemma and estimates of coefficients for regular functions with free domain of definition”, Sb. Math., 196:11 (2005), 1605–1625