Maximal regularity for perturbed integral equations on the line
type: Item
instance of: scholarly article
title: Maximal regularity for perturbed integral equations on the line
zbMATH Open document ID: 1267.45021
author: Carlos Lizama
author: Rodrigo Ponce
published in: Integral Equations and Operator Theory
publication date: 2013-04-15T00:00:00Z
review text: The authors characterize the existence and uniqueness of solutions for a perturbed linear integral equation with infinite delay in Hölder spaces. The method is based on the theory of operator-valued Fourier multipliers. This paper is well written and it is nice to read. We note that the most important tools to prove maximal regularity are Fourier multiplier theorems. They play a key role in the analysis of elliptic and parabolic problems. In particular, the theory of operator-valued Fourier multiplier is applied to obtain results on the hyperbolicity of delay equations, to obtain stability of linear control systems in Banach spaces, to study maximal regularity for difference equations. Some complementary references to this paper are the following: \textit{A. Bátkai, E. Fašanga} and \textit{R. Shvidkoy} [Acta Sci. Math. 69, No. 1--2, 131--145 (2003; Zbl 1050.35120)]; \textit{C. Cuevas} and \textit{C. Vidal} [Adv. Difference Equ. 2006, Article ID 97614, 11 p. (2006; Zbl 1133.39001)]; \textit{A. Castro} and \textit{C. Cuevas} [J. Difference Equ. Appl. 17, No. 3, 327--358 (2011; Zbl 1220.39005)]; \textit{Y. Latushkin} and \textit{F. Räbiger} [Integral Equations Oper. Theory 51, No. 3, 375--394 (2005; Zbl 1077.47042)].
reviewed by: Claudio Cuevas
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 42B15
Mathematics Subject Classification ID: 45A05
zbMATH DE Number: 6153948
zbMATH Keywords: operator-valued Fourier multipliers
zbMATH Keywords: maximal regularity
zbMATH Keywords: linear integral equation
zbMATH Keywords: Hölder spaces
MaRDI profile type: Publication
full work available at URL: s00020-012-2010-8
OpenAlex ID: W2095133048
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DOI: 10.1007/S00020-012-2010-8
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description: scientific article; zbMATH DE number 6153948