In this paper we discuss the relationship between the numerical range of an extensive class of unbounded operator functions and the joint numerical range of the operator coefficients. Furthermore, we derive methods on how to find estimates of the joint numerical range. Those estimates are used to obtain explicitly computable enclosures of the numerical range of the operator function and resolvent estimates. The enclosure and upper estimate of the norm of the resolvent are optimal given the estimate of the joint numerical range.

中文翻译：

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非自伴算子函数的数值范围和可分辨估计的包围

在本文中，我们讨论了广泛的无界算子函数的数值范围与算子系数的联合数值范围之间的关系。此外，我们推导了有关如何找到联合数值范围的估计值的方法。这些估计值用于获得算术函数和可分辨估计值的数值范围的可显式计算的包围物。给定联合数值范围的估计值，则对解析子范数的包围和上估计值是最佳的。