Bounded Laplace transforms, primitives and semigroup orbits
β Scribed by C. J. K. Batty
- Book ID
- 105755003
- Publisher
- Springer
- Year
- 2003
- Tongue
- English
- Weight
- 107 KB
- Volume
- 81
- Category
- Article
- ISSN
- 0003-889X
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π SIMILAR VOLUMES
Let [ f m ; m # N] be a sequence of functions from [0, ) to a Banach space E. We give a new and essential condition on f m , which is weaker than the usual ``local Lipschitz continuity'' condition, ensuring that the convergence of f m is equivalent to the convergence of their Laplace transforms. Thi
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 o
Necessary and sufficient conditions are given for a Banach-space-valued function f to be the Laplace-Stieltjes transform of a function of bounded variation. These conditions are used to obtain generation theorems for both absolutely continuous integrated semigroups and Abel summable semigroups.