Numerical range and Poncelet property

Hwa Long Gau, Pei Yuan Wu

研究成果: 雜誌貢獻回顧評介論文同行評審

42 引文 斯高帕斯(Scopus)


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(φ). 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(φ), 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(φ) to the infinite-dimensional.

頁(從 - 到)173-193
期刊Taiwanese Journal of Mathematics
出版狀態已出版 - 2003


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