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Inequalities for Entire Functions of Exponential Type
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 1984
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