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Approximations of Laplace transforms and integrated semigroups. (English) Zbl 0977.47034
The authors characterize the convergence (uniform on compact intervals) of a sequence of functions \(f_{m} \in C([0,\infty],X)\), \(X\) a Banach space, by the convergence of their Laplace transform. This improves considerably previous Laplace transform versions of the Trotter-Kato theorem [e.g., B. Hennig and F. Neubrander, Appl. Anal. 49, No. 3-4, 151-170 (1993; Zbl 0791.44002) or C. Lizama, J. Math. Anal. Appl. 18, No. 1, 89-103 (1994; Zbl 0815.47053)] and is applied to the approximation of quite general Cauchy problems.

MSC:
47D62 Integrated semigroups
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