Approximations of Laplace transforms and integrated semigroups
type: Item
instance of: scholarly article
title: Approximations of Laplace transforms and integrated semigroups
zbMATH Open document ID: 0977.47034
author: Jin Liang
author: Ti-Jun Xiao
published in: Journal of Functional Analysis
publication date: 2001-02-14T00:00:00Z
review text: The authors characterize the convergence (uniform on compact intervals) of a sequence of functions \(f_{m} \in C([0,\infty],X)\), \(X\) a Banach space, by the convergence of their Laplace transform. This improves considerably previous Laplace transform versions of the Trotter-Kato theorem [e.g., \textit{B. Hennig} and \textit{F. Neubrander}, Appl. Anal. 49, No. 3-4, 151-170 (1993; Zbl 0791.44002) or \textit{C. Lizama}, J. Math. Anal. Appl. 18, No. 1, 89-103 (1994; Zbl 0815.47053)] and is applied to the approximation of quite general Cauchy problems.
Mathematics Subject Classification ID: 47D62
zbMATH DE Number: 1443266
zbMATH Keywords: Laplace transform
zbMATH Keywords: Trotter-Kato theorem
zbMATH Keywords: approximation of general Cauchyproblems
reviewed by: Rainer Nagel
MaRDI profile type: Publication
OpenAlex ID: W2055386624
cites work: Vector-valued Laplace transforms and Cauchy problems
cites work: Q3830008
cites work: Q4352127
cites work: Q4717352
cites work: Convergence theorems for integrated semigroups
cites work: Trace theorems for holomorphic semigroups and the second order Cauchy problem
cites work: On the convergence and approximation of cosine functions
cites work: Q3721264
cites work: On the convergence of resolvents of operators
cites work: On representations, inversions, and approximations of laplace transforms in banach spaces
cites work: Laplace Transforms and α-Times Integrated Semigroups
cites work: Q5526485
cites work: A proof of the Trotter-Kato theorem on approximation of semi-groups
cites work: Extensions of Trotter's operator semigroup approximation theorems
cites work: A General Theorem on the Convergence of Operator Semigroups
cites work: On the convergence and approximation of integrated semigroups
cites work: The Hille-Yosida and Trotter-Kato theorems for integrated semigroups
cites work: On the convergence of semigroups of linear operators
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Q4001537
cites work: Approximation of operator semi-groups
cites work: What is the Laplace Transform?
cites work: The Cauchy problem for higher-order abstract differential equations
DOI: 10.1006/JFAN.1999.3545
description: scientific article; zbMATH DE number 1443266