Completely monotonic and related functions
type: Item
instance of: scholarly article
title: Completely monotonic and related functions
zbMATH Open document ID: 0889.26008
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-06-23T00:00:00Z
review text: Let \(L^N\) denote the class of functions defined by \[ f\in L^N\Leftrightarrow (-1)^k f^{(k)}(t)\geq 0,\quad \forall t>0,\quad \forall k,\quad 0\leq k\leq N. \] For \(N\to \infty\) we write \(f\in L\); such functions are well known as completely monotonic on \((0,\infty)\). The implication \[ f\in L^N\Rightarrow [\forall \alpha> 1: f^\alpha\in L^N] \] is true for \(0\leq N\leq 5\), but false for \(N\geq 6\), while the implication \[ f\in L\Rightarrow [\forall \alpha>1: f^\alpha\in L^N] \] is true for \(0\leq N\leq 6\), but false for \(N\geq 20\).
Mathematics Subject Classification ID: 26A48
zbMATH DE Number: 1005642
zbMATH Keywords: completely monotonic functions
author: Henk van Haeringen
reviewed by: J. Pečarić
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0443
OpenAlex ID: W2090100933
DOI: 10.1006/JMAA.1996.0443
description: scientific article; zbMATH DE number 1005642