论文标题
在Banach空间上反转操作员铅笔的基本方程式
The fundamental equations for inversion of operator pencils on Banach space
论文作者
论文摘要
我们证明，当且仅当laurent系列的系数满足基本方程系统并且在几何上界限时，我们就证明了线性算子铅笔的分解是对开放环的分析。我们的分析扩展了对基本方程式的早期工作，以包括分解具有孤立基本奇异性的情况。我们找到了分解的封闭形式，并使用基本方程式建立关键光谱分离特性时，当分解仅具有有限数量的孤立奇点。最后，我们证明我们的结果也可以应用于多项式铅笔。
We prove that the resolvent of a linear operator pencil is analytic on an open annulus if and only if the coefficients of the Laurent series satisfy a system of fundamental equations and are geometrically bounded. Our analysis extends earlier work on the fundamental equations to include the case where the resolvent has an isolated essential singularity. We find a closed form for the resolvent and use the fundamental equations to establish key spectral separation properties when the resolvent has only a finite number of isolated singularities. Finally we show that our results can also be applied to polynomial pencils.
