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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Inequalities for entire functions of exponential type
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by T. Genchev PDF
Proc. Amer. Math. Soc. 56 (1976), 183-188 Request permission

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 $|S(\theta )| < |T(\theta )|$ 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.
References
  • R. P. Boas Jr., Inequalities for functions of exponential type, Math. Scand. 4 (1956), 29–32. MR 85343, DOI 10.7146/math.scand.a-10453
  • N. G. de Bruijn, Inequalities concerning polynomials in the complex domain, Nederl. Akad. Wetensch., Proc. 50 (1947), 1265–1272 = Indagationes Math. 9, 591–598 (1947). MR 23380
  • N. Obrechkoff, Sur les racines des equations algébriques, Tôhoku Math. J. 38 (1933), 93-100.
  • Ralph Philip Boas Jr., Entire functions, Academic Press, Inc., New York, 1954. MR 0068627
  • T. G. Genchev, A Gauss-Lucas type theorem on trigonometric polynomials, C. R. Acad. Bulgare Sci. 28 (1975), no. 4, 449–451. MR 487211
  • L. Weisner, On the regional location of the zeros of certain functions, Tôhoku Math. J. 44 (1937), 175-177.
  • N. I. Achieser, Theory of approximation, Frederick Ungar Publishing Co., New York, 1956. Translated by Charles J. Hyman. MR 0095369
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • 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