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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Uniform stability of resolvent families


Authors: Carlos Lizama and Vicente Vergara
Journal: Proc. Amer. Math. Soc. 132 (2004), 175-181
MSC (2000): Primary 45D05, 45N05; Secondary 47D06
Published electronically: June 3, 2003
MathSciNet review: 2021260
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Abstract: In this article we study uniform stability of resolvent families associated to an integral equation of convolution type. We give sufficient conditions for the uniform stability of the resolvent family in Hilbert and Banach spaces. Our main result can be viewed as a substantial generalization of the Gearhart-Greiner-Prüss characterization of exponential stability for strongly continuous semigroups.


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Additional Information

Carlos Lizama
Affiliation: Departamento de Matemática, Universidad de Santiago de Chile, Casilla 307-Correo 2, Santiago, Chile
Email: clizama@usach.cl

Vicente Vergara
Affiliation: Departamento de Matemática, Universidad de Santiago de Chile, Casilla 307-Correo 2, Santiago, Chile
Email: vvergara@usach.cl

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07073-4
PII: S 0002-9939(03)07073-4
Keywords: Uniform stability, resolvent family, abstract integral equations
Received by editor(s): August 7, 2001
Received by editor(s) in revised form: September 5, 2002
Published electronically: June 3, 2003
Additional Notes: The authors were supported in part by FONDECYT Grant #1010675
This work is part of the M.Sc. thesis for the second author
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society