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Inequalities for Entire Functions of Exponential Type

Published online by Cambridge University Press:  20 November 2018

Clément Frappier
Clément Frappier*
Affiliation:
Département de Mathématiques et de Statistique, Université de Montréal, C. P. 6128, Succursale “A” Montréal, Québec, H3C 3J7, Canada
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Abstract

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Bernstein's inequality says that if f is an entire function of exponential type τ which is bounded on the real axis then

Genchev has proved that if, in addition, hf (π/2) ≤0, where hf is the indicator function of f, then

Using a method of approximation due to Lewitan, in a form given by Hörmander, we obtain, to begin, a generalization and a refinement of Genchev's result. Also, we extend to entire functions of exponential type two results first proved for polynomials by Rahman. Finally, we generalize a theorem of Boas concerning trigonometric polynomials vanishing at the origin.

Keywords

30D15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 4 , 01 December 1984 , pp. 463 - 471
Copyright
Copyright © Canadian Mathematical Society 1984

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