Means, generalized divided differences, and intersections of osculating hyperplanes
type: Item
instance of: scholarly article
title: Means, generalized divided differences, and intersections of osculating hyperplanes
zbMATH Open document ID: 0848.26011
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-08-05T00:00:00Z
review text: The author offers a new mean value theorem for functional determinants of extended complete Chebyshev systems [as defined in \textit{S. Karlin} and \textit{W. J. Studden}; ``Tchebycheff systems: With applications in analysis and statistics'' (1966; Zbl 0153.38902), except that there the functional determinants were supposed to be positive, while here only to be nonzero] and, based on this, a result stating essentially that under certain assumptions the \(n\) osculating hyperplanes at a point in the \(n\)-dimensional real space intersect in a single point. This defines \(n\) mean values which generalize several known ones (arithmetic, geometric, harmonic, logarithmic, etc.).
Mathematics Subject Classification ID: 26D20
Mathematics Subject Classification ID: 51M05
zbMATH DE Number: 894223
zbMATH Keywords: means
zbMATH Keywords: functional determinants
zbMATH Keywords: extended complete Chebyshev systems
zbMATH Keywords: osculating hyperplanes
author: Alan Horwitz
reviewed by: János Aczél
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0195
OpenAlex ID: W2046808613
DOI: 10.1006/JMAA.1996.0195
description: scientific article; zbMATH DE number 894223