This article is cited in 9 papers

Application of Conformal Mappings to Inequalities for Trigonometric Polynomials

A. V. Olesov

Maritime State University named after G. I. Nevelskoi

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.

UDC: 512.62+517.54

Received: 21.07.2003

DOI: 10.4213/mzm116

 English version: Mathematical Notes, 2004, 76:3, 368–378

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