The fundamental blossoming inequality in Chebyshev spaces. I: Applications to Schur functions
type: Item
instance of: scholarly article
title: The fundamental blossoming inequality in Chebyshev spaces. I: Applications to Schur functions
zbMATH Open document ID: 1388.41019
author: Rachid Ait-Haddou
author: Marie-Laurence Mazure
published in: Foundations of Computational Mathematics
publication date: 2018-03-13T00:00:00Z
review text: The classical Chebyshev theorem says how to obtain the minimum and maximum values of a symmetric multiaffine function of \(n\) variables with a prescribed sum. It is shown that, given two functions in an extended Chebyshev space good for design, a similar result can be stated for the minimum and maximum values of the blossom of the first function with a prescribed value for the blossom of the second one. Moreover, a simple geometric condition on the control polygon of the planar parametric curve defined by the pair of functions ensuring the uniqueness of the solution to the corresponding optimization problem is given. This provides a fundamental blossoming inequality associated with each extended Chebyshev space good for design. This inequality proves to be a tool to derive some new inequalities involving Schur functions which generalize the classical MacLaurin's and Newton's inequalities.
reviewed by: Yuri A. Farkov
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 6849390
zbMATH Keywords: extended Chebyshev spaces
zbMATH Keywords: Chebyshevian blossoming
zbMATH Keywords: MacLaurin's inequalities
zbMATH Keywords: Newton's inequalities
zbMATH Keywords: Müntz spaces
zbMATH Keywords: normalized Schur functions
MaRDI profile type: Publication
full work available at URL: s10208-016-9334-8
OpenAlex ID: W2533722104
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DOI: 10.1007/S10208-016-9334-8
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description: scientific article; zbMATH DE number 6849390