Inequalities for Entire Functions of Exponential Type

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.