Exponential convexity and total positivity
type: Item
instance of: scholarly article
title: Exponential convexity and total positivity
zbMATH Open document ID: 1444.26009
author: Nadezhda Olegovna Kotelina
author: A. B. Pevnyj
publication date: 2020-07-21T00:00:00Z
review text: Let \(I\) be one of the intervals \((0,\infty)\) and \((-\infty,\infty)\) and let \(f:I\rightarrow\mathbb{R}\) be a function associated to a continuous weight \(p:(a,b)\rightarrow\mathbb{R}_{+}\) via the formula \(f(x)=\int_{a}^{b}e^{xt}p(t)\mathrm{d}t.\) The main result of the paper under review is Theorem 2, that asserts that the kernel \(K(x,y)=f(x+y)\) is totally positive on \(I\times I\) (that is, \(\det[f(x_{i}+y_{j})]_{i,j=1}^{n}>0\) for all integers \(n\geq1\) and all families of points \(x_{1}\) \(<\cdots<\) \(x_{n}\) and \(y_{1}<\cdots<y_{n}\) in \(I).\) Several examples illustrating this result are included.
Mathematics Subject Classification ID: 26A51
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 44A10
zbMATH DE Number: 7223664
zbMATH Keywords: exponential convexity
zbMATH Keywords: total positivity
zbMATH Keywords: kernel
MaRDI profile type: Publication
full work available at URL: semi.2020.17.057
OpenAlex ID: W3036266074
Wikidata QID: Q115488141
cites work: Q4914050
cites work: Multivariate characteristic and correlation functions
cites work: Exponential convexity induced by Steffensen's inequality and positive measures
cites work: Q3651574
DOI: 10.33048/SEMI.2020.17.057
published in: Sibirskie Elektronnye Matematicheskie Izvestiya
description: scientific article; zbMATH DE number 7223664