A functional calculus for almost sectorial operators and applications to abstract evolution equations
A functional calculus for almost sectorial operators and applications to abstract evolution equations
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DOI：
10.1007/s00028-002-8079-9
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发表时间：
2002-03
影响因子：
1.4
通讯作者：
F. Periago;B. Straub
中科院分区：
文献类型：
--
作者：
F. Periago;B. Straub
本文对谱位于复平面的一个扇区内，且其预解式对某些和全部z满足扇区外的线性算子A构造了一个泛函演算。借助于这种泛函演算，我们定义了与A及其某些幂相关的复幂和半群。最后，应用这些抽象结果证明了三类不同类型的抽象微分方程古典解的存在唯一性。
In this paper, we construct a functional calculus for linear operatorsAwhose spectrum lies in a sector of the complex plane and whose resolvent satisfiesfor someand allzoutside the sector. By means of this functional calculus, we define complex powers and semigroups associated withAand some of its powers. Finally, these abstract results are applied to prove existence and uniqueness of classical solutions for three different types of abstract differential equations.