Local \(C\)-cosine families and \(n\)-times integrated local cosine families
type: Item
instance of: scholarly article
title: Local \(C\)-cosine families and \(n\)-times integrated local cosine families
zbMATH Open document ID: 1080.34045
author: Xianqiang Yang
published in: Taiwanese Journal of Mathematics
publication date: 2005-03-21T00:00:00Z
review text: For the investigation of ill-posed first-order abstract Cauchy problems, the theory of \(C\)-semigroups and \(n\)-times integrated semigroups has been developed and intensively studied in the last 20 years. The main technical tool in these investigations was the exhausting use of vector-valued Laplace transforms theory. Recently, an analogous line of investigations has been started to investigate second-order (in time) abstract Cauchy problems. The paper under review continues these investigations and develops a theory for local \(C\)-cosine families and \(n\)-times integrated local cosine families. Here, the word ``local'' refers to the fact that the cosine family may be only defined on a finite time interval. Generation theorems for the complete infinitesimal generator in analogy with the Hille-Yosida theory for \(C_0\)-semigroups are proven.
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 47D09
zbMATH DE Number: 2148914
zbMATH Keywords: Laplace transforms
zbMATH Keywords: cosine families
reviewed by: András Bátkai
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500407671
OpenAlex ID: W4242595427
DOI: 10.11650/TWJM/1500407671
description: scientific article; zbMATH DE number 2148914