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Exact estimates for Faber polynomials and for norm of Faber operator

Fahreddin ABDULLAYEV

Exact estimates for Faber polynomials, norm of Faber operator, and -norm of the generating function for the sequence of Faber operator of univalent functions of class sigma are found. The description of continua of the complex plane for which the norm of Faber operator take the value 1 or 3 is obtained.

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Faber polynomials with common zero

Fahreddin ABDULLAYEV | Meerim İmaş Kızı

We describe the set of meromorphic univalent functions in the class Σ, for which the sequence of the Faber polynomials {Fj}∞j=1 have the roots with following properties |Fn(z0)|>0=∑j=1j≠n|Fj(z0)|. For such functions we found an explicit form of the Faber polynomials as well as we discussed some properties.

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