标题： $\mathrm{C}$-局部凸空间上算子半群的最大正则性 显示英文标题

标题： $\mathrm{C}$-maximal regularity for operator semigroups on locally convex spaces

摘要： 我们研究局部凸空间上强连续半群关于连续函数的最大正则性及其与可接受算子概念之间的关系。 这扩展了经典巴拿赫空间上强连续半群的几个结果。 特别是，我们证明了 利用有界半变差概念对$\mathrm{C}$-最大正则性的特拉维斯表征可以推广到一般情况。 在一些拓扑假设下，我们进一步证明了在此背景下最大正则性和可接受性之间的等价性。 显示英文摘要

摘要： We study maximal regularity with respect to continuous functions for strongly continuous semigroups on locally convex spaces as well as its relation to the notion of admissible operators. This extends several results for classical strongly continuous semigroups on Banach spaces. In particular, we show that Travis' characterization of $\mathrm{C}$-maximal regularity using the notion of bounded semivariation carries over to the general case. Under some topological assumptions, we further show the equivalence between maximal regularity and admissibility in this context.