FINITE AND LOCAL LAPLACE TRANSFORMS IN BANACH SPACES

[摘要] We establish two characterizations of local Laplace transforms in Banach spaces. The first result follows the classic approach of Widder, while the second is in terms of vector-valued moment sequences. As a consequence, we derive characterizations of nilpotent semigroups.AMS 2000 Mathematics subject classification: Primary 44A10; 47D03

[学科分类] 数学（综合）

[关键词] local Laplace transform;finite Laplace transform;nilpotent semigroup;moment sequence