標題: Numerical range and Poncelet property
作者: Gau, HL
Wu, PY
應用數學系
Department of Applied Mathematics
關鍵字: numerical range;Poncelet property;unitary dilation
公開日期: 1-Jun-2003
摘要: 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 reftiting 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.
URI: http://hdl.handle.net/11536/27801
ISSN: 1027-5487
期刊: TAIWANESE JOURNAL OF MATHEMATICS
Volume: 7
Issue: 2
起始頁: 173
結束頁: 193
Appears in Collections:Articles