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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:
 45N05 Abstract integral equations, integral equations in abstract spaces 45D05 Volterra integral equations 47D03 Groups and semigroups of linear operators
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##### References:
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