Estimates for the imaginary parts of the zeros of a polynomial

Giroux, André

doi:10.1090/S0002-9939-1974-0333566-5

Estimates for the imaginary parts of the zeros of a polynomial
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by André Giroux PDF

Proc. Amer. Math. Soc. 44 (1974), 61-67 Request permission

Abstract:

Estimates for the imaginary parts of the zeros of a polynomial are obtained as a function of its ${L^2}$ norm on an interval with respect to an arbitrary weight. The resulting inequality is sharp. Orthogonal polynomials with respect to the given weight are used as the main tool. Simple consequences are deduced and ${L^p}$ norms are also considered.

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Sur l’algèbre fonctionnelle

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