An Inequality for Derivatives of Polynomials Whose Zeros Are in a Half-plane
نویسندگان
چکیده
Let Q be a real polynomial of degree N all of whose zeros lie in the half-plane Re z < 0. Let M(r, Q) be the maximum of | Q(z) | on \z\= r and n(r,0) the counting function of the zeros of Q. It is shown that the inequality M(r, Q') « (2r)"'{A' + n(r,0)}M(r, Q) holds for r > 0. It is also shown that Bernstein's inequality characterizes polynomials.
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