Ellipses and compositions of finite Blaschke products

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• 作者：Pamela Gorkin^a ; ¹ ; ^{pgorkin@bucknell.edu" class="auth_mail" title="E-mail the corresponding author} ; Nathan Wagner^b ; ^{naw006@bucknell.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Blaschke product ; Poncelet curve ; Numerical range ; Compression of the shift operator
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：445
• 期：2
• 页码：1354-1366
• 全文大小：506 K

文摘

We provide a new proof of a theorem of Fujimura characterizing Blaschke products of degree-4 that are compositions of two degree-2 Blaschke products, connect this result to the numerical ranges of certain operators, and characterize Poncelet ellipses that are inscribed in quadrilaterals geometrically and algebraically.