On the polynomials with all their zeros on the unit circle
type: Item
instance of: scholarly article
title: On the polynomials with all their zeros on the unit circle
zbMATH Open document ID: 0822.30008
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-06-08T00:00:00Z
review text: The author shows that a polynomial has the title property if and only if it has the form \(z^ m q(z) + e^{i \theta} q^* (z)\), where \(q(z)\) is a polynomial with all zeros within the closed unit disc and \(q^* (z)\) is its reciprocal polynomial. From this he derives sufficient conditions on the coefficients of a real polynomial (loosely, symmetry and zigzag) that its zeros lie on the unit circle. Examples are given.
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 12D10
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 762184
zbMATH Keywords: Schur-Cohn condition
zbMATH Keywords: Eneström-Kakeya condition
zbMATH Keywords: reciprocal polynomial
author: Weiyu Chen
reviewed by: Edward J. Barbeau
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1105
OpenAlex ID: W2062373969
DOI: 10.1006/JMAA.1995.1105
description: scientific article; zbMATH DE number 762184