Laplace Transforms and Integrated, Regularized Semigroups in Locally Convex Spaces
✍ Scribed by Xiao Tijun; Liang Jin
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 447 KB
- Volume
- 148
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
In this paper, we consider the vector-valued Laplace transforms, r-times (r # [0, )) integrated semigroups and regularized semigroups in the context of sequentially complete locally convex spaces. Our theorems develop the corresponding results in [1,11], including the well known integrated version of the classical Widder's representation theorem of Laplace transforms for functions taking values in Banach spaces. Moreover, we study a class of differential operators on certain function spaces. Optimal conditions, making them the generators of integrated or regularized semigroups, are obtained. We finally show some applications to abstract Cauchy problems. 1997 Academic Press [24], S. Zaidman [40] proved in 1960 that Widder's theorem holds in a Banach space X if and only if X has the Radon Nikodym property. In 1987, W. Arendt [1] present a significant integrated version of Widder's theorem in an arbitrary Banach space X: article no. FU973096