论文标题
在规范矢量空间中强连续分数半群的内在特性
Intrinsic properties of strongly continuous fractional semigroups in normed vector spaces
论文作者
论文摘要
在许多情况下，已经成功地研究了强烈连续半群的规范估计值，但是目前在奇异积分方程的解决方案操作员的情况下尚无相应的研究。这些方程式最近引起了很大的兴趣，因为它们有可能通过纳入所谓的非本地效应来对众多物理相关现象进行建模，并提高准确性。在本文中，我们提供了为特定类别的操作员提供此类估算的方向的第一步，这些操作员用作某些积分方程的解决方案。提供的结果在任意规范的矢量空间中保留，并将强烈连续半群的经典结果作为特殊情况。
Norm estimates for strongly continuous semigroups have been successfully studied in numerous settings, but at the moment there are no corresponding studies in the case of solution operators of singular integral equations. Such equations have recently garnered a large amount of interest due to their potential to model numerous physically relevant phenomena with increased accuracy by incorporating so-called non-local effects. In this article, we provide the first step in the direction of providing such estimates for a particular class of operators which serve as solutions to certain integral equations. The provided results hold in arbitrary normed vector spaces and include the classical results for strongly continuous semigroups as a special case.
