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 Mat. Sb., 2014, Volume 205, Number 10, Pages 47–76 (Mi msb8146)

Inequalities for majorizing analytic functions and their applications to rational trigonometric functions and polynomials

A. V. Olesov

Maritime State University named after G. I. Nevelskoi

Abstract: New inequalities are established for analytic functions satisfying Meiman's majorization conditions. Estimates for values of and differential inequalities involving rational trigonometric functions with an integer majorant on an interval of length less than the period and with prescribed poles which are symmetrically positioned relative to the real axis, as well as differential inequalities for trigonometric polynomials in some classes, are given as applications. These results improve several theorems due to Meiman, Genchev, Smirnov and Rusak.
Bibliography: 27 titles.

Keywords: majorizing analytic functions, entire functions of exponential type, rational trigonometric functions, polynomials, Bernstein-type inequalities.

 Funding Agency Grant Number Russian Foundation for Basic Research 11-01-00038 Far Eastern Branch of the Russian Academy of Sciences 12-II-ÑÎ-01Ì-002

DOI: https://doi.org/10.4213/sm8146

Full text: PDF file (697 kB)
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English version:
Sbornik: Mathematics, 2014, 205:10, 1413–1441

Bibliographic databases:

UDC: 517.54+517.535
MSC: 30C10, 30C80

Citation: A. V. Olesov, “Inequalities for majorizing analytic functions and their applications to rational trigonometric functions and polynomials”, Mat. Sb., 205:10 (2014), 47–76; Sb. Math., 205:10 (2014), 1413–1441

Citation in format AMSBIB
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