Resolvent representations for functions of sectorial operators
Resolvent representations for functions of sectorial operators
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DOI：
10.1016/j.aim.2016.12.009
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发表时间：
2016-02
期刊：
影响因子：
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通讯作者：
C. Batty;A. Gomilko;Y. Tomilov
中科院分区：
文献类型：
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作者：
C. Batty;A. Gomilko;Y. Tomilov
我们得到了Banach空间上的扇形算子A和右半平面及右半轴的全纯映射A的预解式的积分表示.作为推论，对于一个广泛的函数类，我们证明了：当− A在Banach空间上生成一个扇形有界全纯C 0-半群时，算子− A（A）生成一个扇形有界全纯C 0-半群，并且A的扇形角保持不变。当λ是一个伯恩斯坦函数时，这是最近由Gomilko和Tomilov证明的，但这里的证明更直接。此外，我们证明了A的这种持久性至少在Hilbert空间上可以用A的有界H∞-演算的存在性来描述。作为我们的方法的副产品，我们还获得了新的结果的功能映射到生成的有界半群的生成元的全纯半群和从属的Ritt算子。
We obtain integral representations for the resolvent of ψ (A), where ψ is a holomorphic function mapping the right half-plane and the right half-axis into themselves, and A is a sectorial operator on a Banach space. As a corollary, for a wide class of functions ψ, we show that the operator− ψ (A) generates a sectorially bounded holomorphic C 0-semigroup on a Banach space whenever− A does, and the sectorial angle of A is preserved. When ψ is a Bernstein function, this was recently proved by Gomilko and Tomilov, but the proof here is more direct. Moreover, we prove that such a permanence property for A can be described, at least on Hilbert spaces, in terms of the existence of a bounded H∞-calculus for A. As byproducts of our approach, we also obtain new results on functions mapping generators of bounded semigroups into generators of holomorphic semigroups and on subordination for Ritt operators.