Faber polynomials with common roots

• Дата: 2014
• Автори: Savchuk, V. V., Савчук, В. В.
• Формат: Стаття
• Мова: Українська
• Опубліковано: Інститут математики НАН України 2014
• Онлайн доступ: https://trim.imath.kiev.ua/index.php/trim/article/view/78
• Назва журналу: Transactions of Institute of Mathematics of NAS of Ukraine

We describe two sets of meromorphic univalent functions in the class $\Sigma$, for which the sequences of Faber polynomials $\{F_j\}_{j=1}^\infty $ have the roots with following properties respectively: $\sum_{j=1}^{n}|F_j(z_0)|=0<|F_{n+1}(z_0)|, $ $n\in\mathbb N, $ and ${|F_1(z_0)|&a...