论文标题
伪数字范围和光谱外壳
Pseudo Numerical Ranges and Spectral Enclosures
论文作者
论文摘要
我们介绍了用于操作员功能的PSEU \ - DO数值范围的新概念，以及sesquilinear forms的家族以及$ n \ times n $运算符矩阵函数的pseu \ -do块数值范围。尽管这些概念即使在有限的情况下也是新的，但我们涵盖了具有无限系数，无限型全体形态（a）类型（a）类型的无限型全体形态的多项式和（b）类型的操作员家族的多项式。我们的主要结果包括伪数值范围和伪块数值范围的光谱包容性能。对于对角占主导地位和非对角线主导的操作员矩阵，它们使我们能够根据Schur补充的伪数值范围证明光谱围栏，而Schur补语不再需要优势订单$ 0 $，甚至不需要$ <1 $。作为一种应用，我们为线性阻尼的波动方程建立了一种新型的光谱边界，并可能无限和/或奇异阻尼。
We introduce the new concepts of pseu\-do numerical range for operator functions and families of sesquilinear forms as well as the pseu\-do block numerical range for $n \times n$ operator matrix functions. While these notions are new even in the bounded case, we cover operator polynomials with unbounded coefficients, unbounded holomorphic form families of type (a) and associated operator families of type (B). Our main results include spectral inclusion properties of pseudo numerical ranges and pseudo block numerical ranges. For diagonally dominant and off-diagonally dominant operator matrices they allow us to prove spectral enclosures in terms of the pseudo numerical ranges of Schur complements that no longer require dominance order $0$ and not even $<1$. As an application, we establish a new type of spectral bounds for linearly damped wave equations with possibly unbounded and/or singular damping.
