NUMERICAL RANGE AND PONCELET PROPERTY
NUMERICAL RANGE AND PONCELET PROPERTY
复制标题
数值范围和 PONCELET 属性
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
P. Wu
中科院分区：
文献类型：
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作者：
Hwa;P. Wu
在这篇综述文章中，我们给出了一个简要的说明最近的事态发展的庞斯莱性质的数值范围的压缩移位$S（\phi）$。它可以被认为是第二作者在美国数学月刊上发表的关于这个主题的最新文章的更新和更高级的版本。新信息包括：（1）主要结果的简化方法（Poncelet，Brianchon-Ceva和Lucas-Siebeck定理的推广），（2）Mirman最近的发现反驳了以前关于Poncelet曲线与有限维S（\phi）数值域边界重合的猜想，（3）本文作者将上述结果从酉膨胀到正规膨胀，以及从有限维S（\phi）到无穷维的部分推广。立体的
In this survey article, we give an expository account of the recent developments on the Poncelet property for numerical ranges of the compressions of the shift $S(\phi)$. It can be considered as an updated and more advanced edition of the recent expository article published in the American Mathematical Monthly by the second author on this topic. The new information includes: (1) a simplified approach to the main results (generalizations of Poncelet, Brianchon--Ceva and Lucas--Siebeck theorems) in this area, (2) the recent discovery of Mirman refuting a previous conjecture on the coincidence of Poncelet curves and boundaries of the numerical ranges of finite-dimensional $S(\phi)$, and (3) some partial generalizations by the present authors of the above-mentioned results from the unitary-dilation context to the normal-dilation one and also from the finite-dimensional $S(\phi)$ to the infinite-dimensional.