Vector-valued laplace transforms and cauchy problems
Vector-valued laplace transforms and cauchy problems
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DOI：
10.1007/bf02774144
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发表时间：
2002-11
影响因子：
1
通讯作者：
W. Arendt
中科院分区：
文献类型：
--
作者：
W. Arendt
利用拉普拉斯变换系统地研究了Banach空间中的线性微分方程.中心工具是Widder定理（描述有界函数的拉普拉斯变换）的“集成版本”。它在任何Banach空间中成立（而Widder定理的向量值版本本身成立，当且仅当Banach空间具有Radon-Nikodym性质）。希勒-吉田定理和其他生成定理是直接的结果。本文提出的方法可应用于定义域不稠密的算子。
Linear differential equations in Banach spaces are systematically treated with the help of Laplace transforms. The central tool is an “integrated version” of Widder’s theorem (characterizing Laplace transforms of bounded functions). It holds in any Banach space (whereas the vector-valued version of Widder’s theorem itself holds if and only if the Banach space has the Radon-Nikodým property). The Hille-Yosida theorem and other generation theorems are immediate consequences. The method presented here can be applied to operators whose domains are not dense.