A characterization of uniform continuity for Volterra equations in Hilbert spaces

Lizama, Carlos

doi:10.1090/S0002-9939-98-04594-8

A characterization of uniform continuity for Volterra equations in Hilbert spaces
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Proc. Amer. Math. Soc. 126 (1998), 3581-3587 Request permission

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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