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Regularized solutions for abstract Volterra equations. (English) Zbl 0952.45005
The author shows the existence, the uniqueness, and some qualitative properties of solutions for the abstract Volterra equation $$u(t) = f(t) + \int_{0}^{t}a(t-s)Au(s) ds,\quad t\in [0,T]$$ on a complex Banach space $X$ by means of an extended notion of resolvent, where $A$ is a closed linear unbounded operator with domain $D(A)$, $a \not=0$ is a scalar kernel, and $f \in C([0,T],X)$.

MSC:
45N05Abstract integral equations, integral equations in abstract spaces
45D05Volterra integral equations
47D03(Semi)groups of linear operators
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References:
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