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Estimates for the imaginary parts of the zeros of a polynomial


Author: André Giroux
Journal: Proc. Amer. Math. Soc. 44 (1974), 61-67
MSC: Primary 42A56; Secondary 30A08
DOI: https://doi.org/10.1090/S0002-9939-1974-0333566-5
MathSciNet review: 0333566
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0333566-5
Keywords: Zeros of polynomials, imaginary parts, weight function, $ {L^p}$ norms, orthogonal polynomials, derivative of a polynomial, Gauss quadrature formula, Riesz-Thorin's inequality, Hausdorff-Young's inequality
Article copyright: © Copyright 1974 American Mathematical Society

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