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A characterization of uniform continuity for Volterra equations in Hilbert spaces. (English) Zbl 0905.47028
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:
47D06 One-parameter semigroups and linear evolution equations
47A50 Equations and inequalities involving linear operators, with vector unknowns
47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
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