Enclosure of the Numerical Range of a Class of Non-selfadjoint Rational Operator Functions
Enclosure of the Numerical Range of a Class of Non-selfadjoint Rational Operator Functions
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DOI：
10.1007/s00020-017-2378-6
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发表时间：
2017-06-01
影响因子：
0.8
通讯作者：
Torshage, Axel
中科院分区：
文献类型：
--
作者：
Engstrom, Christian;Torshage, Axel
本文介绍了一类有理数算子函数的数值范围的包络。与数值范围相反，所提出的外壳可以在无限维情况下以及在有限维情况下精确计算。此外，仅给定算符系数的数值范围，新外壳是最小的，并且通过研究外壳可以获得数值范围的许多特性。我们引入了一个伪数值范围，并研究了该集合的一个封闭。这个附图提供了解析范数的可计算上界。
In this paper we introduce an enclosure of the numerical range of a class of rational operator functions. In contrast to the numerical range the presented enclosure can be computed exactly in the infinite dimensional case as well as in the finite dimensional case. Moreover, the new enclosure is minimal given only the numerical ranges of the operator coefficients and many characteristics of the numerical range can be obtained by investigating the enclosure. We introduce a pseudonumerical range and study an enclosure of this set. This enclosure provides a computable upper bound of the norm of the resolvent.