THE HILLE–YOSIDA THEOREM FOR LOCAL CONVOLUTED SEMIGROUPS

Proceedings of the Edinburgh Mathematical Society

Valentin Keyantuo¹ 

[1] Claus Müller

关键词: local Laplace transform;    local convoluted semigroup;    integrated semigroup;    distribution semigroup;    ultradistribution semigroup.;   

DOI  :  10.1017/S0013091500001103

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

The characterization theorem for the Banach-space-valued local Laplace transform established by Keyantuo, Müller and Vieten is used to obtain a real variable characterization of generators of local convoluted semigroups. The concept of local convoluted semigroups extends that of distribution as well as ultradistribution semigroups. Complete characterizations existed only for exponentially bounded semigroups integrated $alpha$ times, whereas for the non-exponential case generation results had been obtained in terms of complex conditions only.AMS 2000 Mathematics subject classification: Primary 47D03; 47D06; 44A10

【 授权许可】

Unknown