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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Inequalities for entire functions of exponential type


Author: T. Genchev
Journal: Proc. Amer. Math. Soc. 56 (1976), 183-188
MSC: Primary 30A66; Secondary 42A04
DOI: https://doi.org/10.1090/S0002-9939-1976-0414871-2
MathSciNet review: 0414871
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Abstract: This paper is concerned with a class of linear operators acting in the space of the trigonometric polynomials and preserving the inequalities of the form $ \vert S(\theta )\vert < \vert T(\theta )\vert$ in the half plane $ {\text{Im}}\theta > 0$. Some inequalities for entire functions of exponential type and some theorems concerning the distribution of the zeros of the trigonometric polynomials, including an analogue to the Gauss-Lucas theorem, are derived.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0414871-2
Keywords: Inequalities in the complex domain, trigonometric polynomials, extremal problems
Article copyright: © Copyright 1976 American Mathematical Society