We describe the set of meromorphic univalent functions in the class \(\Sigma \), for which the sequence of the Faber polynomials \(\{F_j\}_{j=1}^\infty \) have the roots with following properties \(|F_n (z_0)|>0=\sum _{\begin{array}{c} j=1 \\ j\not =n \end{array}}|F_j (z_0 )|\). For such functions we found an explicit form of the Faber polynomials as well as we discussed some properties.

中文翻译：

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费伯多项式为零

我们在类\（\ Sigma \）中描述亚纯一价函数集，为此，Faber多项式\（\ {F_j \} _ {j = 1} ^ \ infty \）的序列具有以下性质\（| F_n（z_0）|> 0 = \ sum _ {\ begin {array} {c} j = 1 \\ j \ not = n \ end {array}} | F_j（z_0）| \）。对于此类函数，我们找到了Faber多项式的显式形式，并讨论了一些属性。