Estimates for the imaginary parts of the zeros of a polynomial-Reference-Cited by-同舟云学术

Estimates for the imaginary parts of the zeros of a polynomial

Published:1974 Issue:1 Volume:44 Page:61-67
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Giroux André

Abstract

Estimates for the imaginary parts of the zeros of a polynomial are obtained as a function of its L 2 {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 {L^p} norms are also considered.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1974-044-01/S0002-9939-1974-0333566-5/S0002-9939-1974-0333566-5.pdf

Reference11 articles.

1. On the zeros of a polynomial and of its derivative. II;de Bruijn, N. G.;Nederl. Akad. Wetensch., Proc.,1947

2. Die Lage der Nullstellen eines Polynoms;Specht, Wilhelm;Math. Nachr.,1956

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Coherent pairs of measures of the second kind on the real line and Sobolev orthogonal polynomials. An application to a Jacobi case;Studies in Applied Mathematics;2023-05-22

2. Orthogonal Expansion of Real Polynomials, Location of Zeros, and an L2 Inequality;Journal of Approximation Theory;2001-03

3. Inequalities for Polynomial Zeros;Survey on Classical Inequalities;2000

4. Inequalities for the Zeros of an Orthogonal Expansion of a Polynomial;Recent Progress in Inequalities;1998

5. Polynomials orthogonal on a circular arc;Journal of Computational and Applied Mathematics;1990-08