On self-reciprocal polynomials
type: Item
instance of: scholarly article
title: On self-reciprocal polynomials
zbMATH Open document ID: 0907.30007
DOI: 10.1007/BF02867257
author: A. Aziz
author: B. A. Zargar
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1999-02-24T00:00:00Z
review text: A polynomial \(P(z)\) of degree \(n\) is said to be self-reciprocal when it satisfies \(z^nP(1/z)=P(z)\) for all complex \(z\). The authors' result can be stated most easily using as norm \(\| Q\| \) of a polynomial \(Q\) the \(L^2\) norm of \(Q(e^{it})\) on \([0,2\pi]\). Theorem: If \(P(z)\) is a self-reciprocal polynomial of degree at most \(n\) then \(n/2 \leq \| P'\| /\| P\| \leq n/ \sqrt 2 \). Both estimates are sharp.
Mathematics Subject Classification ID: 30C10
zbMATH DE Number: 1192589
zbMATH Keywords: self-reciprocal polynomials
zbMATH Keywords: \(L^2\) estimates
zbMATH Keywords: inequalities
reviewed by: Rudolf Wegmann
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02867257
OpenAlex ID: W2093979627
description: scientific article; zbMATH DE number 1192589