A GENERAL FRAMEWORK FOR HOLOMORPHIC FUNCTIONAL CALCULI
A GENERAL FRAMEWORK FOR HOLOMORPHIC FUNCTIONAL CALCULI
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全纯函数计算的通用框架
DOI：
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发表时间：
2005
影响因子：
0.7
通讯作者：
M. Haase
中科院分区：
文献类型：
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作者：
M. Haase
摘要给出了构造无界算子全纯泛函微积分的一个抽象方法，并将其应用于扇形算子的特殊情况。实际上，我们得到了一个比以前已知的更大的函数类的微积分，包括某些亚纯函数。我们讨论了拓扑的作用。然后详细证明了一个复合规则$(fcirc g)(a)=f(g(a))$，这是本文的主要结果。这是这样做的，证明可以很容易地转移到其他类算子的函数演算。
Abstract We present an abstract approach to the construction of holomorphic functional calculi for unbounded operators and apply it to the special case of sectorial operators. In effect, we obtain a calculus for a much larger class of functions than was known before, including certain meromorphic functions. We discuss the role of topology. Then we prove in detail a composition rule $(fcirc g)(A)=f(g(A))$ which is the main result of the paper. This is done in such a way that the proof can easily be transferred to functional calculi for other classes of operators.