An exact inequality for the derivative of a trigonometric polynomial having only real zeros
type: Item
instance of: scholarly article
title: An exact inequality for the derivative of a trigonometric polynomial having only real zeros
zbMATH Open document ID: 0616.42001
DOI: 10.1007/BF01170244
author: S. A. Pichugov
author: V. F. Babenko
published in: Mathematical Notes
publication date: 1986-01-01T00:00:00Z
review text: The following theorem is proved: If a trigonometric polynomial \(T_ n\) has exactly 2n zeros (in \([-\pi,\pi]\)) then \(\| T_ n'\| \geq n/2\cdot (1-1/2n)^{n-}\cdot \| T_ n\|\) and, moreover, the above inequality becomes an equality only for the polynomials of the form \(T_ n(x)=a\cdot (\sin (x-\gamma)/2)^{2n}.\)
Mathematics Subject Classification ID: 42A05
zbMATH DE Number: 3998430
zbMATH Keywords: trigonometric polynomial
reviewed by: Jacek Jędrzejewski
MaRDI profile type: Publication
cites work: Q3663911
description: scientific article; zbMATH DE number 3998430