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Zbl 0905.47028
Lizama, Carlos
A characterization of uniform continuity for Volterra equations in Hilbert spaces. (English)
[J] Proc. Am. Math. Soc. 126, No.12, 3581-3587 (1998). ISSN 0002-9939; ISSN 1088-6826/e

Summary: 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.
MSC 2000:
*47D06 One-parameter semigroups and linear evolution equations
47A50 Equations and inequalities involving linear operators
47A56 Functions whose values are linear operators

Keywords: Volterra equations; resolvent equation; uniform continuity; Laplace transform; norm continuity; holomorphic operator family

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