Estimation of the rate of convergence of semigroups to an asynchronous equilibrium
type: Item
instance of: scholarly article
title: Estimation of the rate of convergence of semigroups to an asynchronous equilibrium
zbMATH Open document ID: 0972.47028
DOI: 10.1007/PL00006020
published in: Semigroup Forum
publication date: 2001-11-02T00:00:00Z
review text: Denote \(T(t)\) the semigroup of linear operators defined on some Banach space \(B\). Asynchronous exponential growth occurs when one can determine a pair \((\lambda_0,v)\), \(\lambda_0\in{\mathbb{R}}\), \(0\neq v\in B\), such that \(e^{-\lambda_0 t}T(t)x - c v\to 0\) as \(t\to +\infty\) for every \(x\in B\) and some \(c\in{\mathbb{R}}\). The main result of the paper is an estimate of the rate of convergence of \(T(t)\) to an asynchronous equilibrium. The particular case of translation semigroups is examined. The results obtained are applied to an equation in demography.
reviewed by: Michael Perelmuter
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 1523489
zbMATH Keywords: asynchronous exponential growth
zbMATH Keywords: asynchronous equilibrium
zbMATH Keywords: translation semigroups
author: Mohamed Khaladi
author: Ovide Arino
MaRDI profile type: Publication
full work available at URL: pl00006020
OpenAlex ID: W2063787523
description: scientific article; zbMATH DE number 1523489