Approximations of Laplace transforms and integrated semigroups
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., \textit{B. Hennig} and \textit{F. Neubrander}, Appl. Anal. 49, No. 3-4, 151-170 (1993; Zbl 0791.44002) or \textit{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.
scientific article; zbMATH DE number 1443266
scientific article