更新至：谱集：数值域及其推广

中文摘要 AI 辅助

我们利用Lorist和Schwenninger的结果（{\em 关于Crouzeix猜想的解答}，arXiv:2608.03841v2，https://arxiv.org/abs/2608.03841）来更新Crouzeix和Greenbaum于2019年发表的论文（{\em 谱集：数值域及其推广}，SIAM J.~Matrix Anal.~Appl., 40(3):1087-1101）。对于2019年论文中考虑的所有区域，我们能够证明该区域是一个$K$-谱集，且其$K$的上界小于2019年论文中确立的上界。特别地，我们证明各种环形区域是$2$-谱集，而带有圆形孔洞或切口的更一般凸区域是$4$-谱集。

英文摘要

We use the results of Lorist and Schwenninger, {\em A solution to Crouzeix's conjecture}, arXiv:2608.03841v2, https://arxiv.org/abs/2608.03841, to update the 2019 paper of Crouzeix and Greenbaum, {\em Spectral sets: Numerical range and beyond}, SIAM J.~Matrix Anal.~Appl., 40(3):1087-1101. For all regions considered in the 2019 paper, we are able to show that the region is a $K$-spectral set with a bound on $K$ that is smaller than that established in the 2019 paper. In particular, we show that various annular regions are $2$-spectral sets and that a more general convex region with a circular hole or cutout is a $4$-spectral set.

发表机构

• Univ. Rennes, CNRS, IRMAR - UMR 6625（雷恩大学）
• University of Washington（华盛顿大学）

机构由 AI 辅助整理，请以论文原文为准。