Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T07:26:21.117Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Elementary Inequalities for Polynomials

Published online by Cambridge University Press:  03 November 2016

W.W. Rogosinski
Get access Rights & Permissions [Opens in a new window]

Extract

1. In this note we consider polynomials of a real variable x and of degree at most n,

The coefficients ak, may be complex. We are given a “mass distribution”, that is, a set of n + 1 real numbers xi, 0 ≤ i ≤ n, such that

Type
Research Article
Information
The Mathematical Gazette , Volume 39 , Issue 327 , February 1955 , pp. 7 - 12
Copyright
Copyright © The Mathematical Association 1955

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Markoff, A. “On a problem of D. J. Mendelejeff”, Bull. Acad. of Science, St. Petersburg, 62 (1899), 1–24 (in Russian).Google Scholar
Markoff, W. “Über Polynome, die in einem gegebenen Intervalle möglichst wenig von Null abweichen,” Math. Ann., 77 (1916), 213–258; translation from Mémoires Acad, of Science, St. Petersburg (1892) (in Russian).CrossRefGoogle Scholar
Pólya, G. and Szegö, G. Aufgaben und Lehrsätze aus der Analysis, II (Berlin, 1925).Google Scholar
Schur, I. “Über das Maximum des absoluten Beitrages eines Polynoms in einem gegebenen Intervalle”, Math. Zeitschr., 4 (1919), 271–287.CrossRefGoogle Scholar
Tchebychef, P.L. Œuvres, I (St. Petersburg, 1899).Google Scholar