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

 

A characterization of uniform continuity
for Volterra equations in Hilbert spaces


Author: Carlos Lizama
Journal: Proc. Amer. Math. Soc. 126 (1998), 3581-3587
MSC (1991): Primary 47D06; Secondary 47A50
MathSciNet review: 1469423
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Abstract: We show that the norm continuity of the resolvent for a Volterra equation of scalar type is equivalent to the decay to zero of a holomorphic operator family along some imaginary axis.


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Additional Information

Carlos Lizama
Affiliation: Department of Mathematics, University of Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile
Email: clizama@fermat.usach.cl

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04594-8
PII: S 0002-9939(98)04594-8
Keywords: Volterra equations, resolvent equation, uniform continuity, Laplace transform
Received by editor(s): May 28, 1996
Received by editor(s) in revised form: April 21, 1997
Additional Notes: This research was done while the author was visiting at the Mathematisches Institut, Universität Tübingen supported by the Alexander von Humboldt Foundation.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society