论文标题
无限运算符的有界功能分解
Bounded functional calculi for unbounded operators
论文作者
论文摘要
本文总结了最近发现的几个无限算子的几个有界功能分解的理论。扩展Hille-phillips-phillips-phillips congulus（负）发电机$ a $ a $ a $ c_0 $ c_0 $ - 序列，尤其是在希尔伯特（Hilbert）空间上的有界半群和Banach Space上有界的Holomormormormormorphic semigroups。它们包括Hille-Phillips类外的功能，并且通常为生成的运营商$ f（a）$的规范提供更清晰的界限。该结石主要基于相关函数类别的适当重现公式，它们依赖于功能理论的重要而有趣的发展。它们与标准功能表兼兼容，并接受适当的收敛引理和光谱映射定理。它们还可以用来得出几种知名的操作员规范估计，提供了其中一些的概括，并扩展了操作员半群的一般理论。我们的目的是帮助读者使用这些微积分，而不必了解其结构的细节。
This article summarises the theory of several bounded functional calculi for unbounded operators that have recently been discovered. The extend the Hille--Phillips calculus for (negative) generators $A$ of certain bounded $C_0$-semigroups, in particular for bounded semigroups on Hilbert spaces and bounded holomorphic semigroups on Banach spaces. They include functions outside the Hille-Phillips class, and they generally give sharper bounds for the norms of the resulting operators $f(A)$. The calculi are mostly based on appropriate reproducing formulas for the relevant classes of functions, and they rely on significant and interesting developments of function theory. They are compatible with standard functional calculi and they admit appropriate convergence lemmas and spectral mapping theorems. They can also be used to derive several well-known operator norm-estimates, provide generalisations of some of them, and extend the general theory of operator semigroups. Our aim is to help readers to make use of these calculi without having to understand the details of their construction.
