Evolution semigroups and sums of commuting operators: A new approach to the admissibility theory of function spaces
type: Item
instance of: scholarly article
title: Evolution semigroups and sums of commuting operators: A new approach to the admissibility theory of function spaces
zbMATH Open document ID: 0966.34049
author: Satoru Murakami
author: Toshiki Naito
author: Nguyen Van Minh
published in: Journal of Differential Equations
publication date: 2001-08-08T00:00:00Z
review text: The authors study the equation \((*)\) \({d}/{dt}\) \(u(t) = Au(t) + f(t)\), where \(A\) is a generator of a \(C_{0}\)-semigroup on a Banach space \(X\), and are interested in which properties of the function \(f\) are inherited by the solution \(u\). To that purpose they consider the generator \(G\) of the evolution semigroup \(T(t)g(s) = e^{tA}g(s-t)\) on \(X\)-valued function spaces on \(\mathbb{R}\). Formally this generator is the sum of \({-d}/{dt}\) and the multiplication operator given by \(A\). They use spectral theory to find criteria for the solvability of \((*)\). The method and the results are also applied to higher-order and functional-differential equations.
reviewed by: Rainer Nagel
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 34K30
zbMATH DE Number: 1515443
zbMATH Keywords: evolution semigroups
zbMATH Keywords: commuting operators
zbMATH Keywords: solvability
MaRDI profile type: Publication
full work available at URL: jdeq.1999.3757
OpenAlex ID: W2093485370
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Evolution semigroups and sums of commuting operators: A new approach to the admissibility theory of function spaces (cites work)
cites work: Q5682669

Evolution semigroups and sums of commuting operators: A new approach to the admissibility theory of function spaces (cites work)
cites work: Q4129765

Evolution semigroups and sums of commuting operators: A new approach to the admissibility theory of function spaces (DOI)
DOI: 10.1006/JDEQ.1999.3757