V. Savchuk

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20152024

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math.CV2024

Best approximations for the weighted combination of the Cauchy--Szegö kernel and its derivative in the mean

Viktor V. Savchuk, Maryna V. Savchuk

In this paper, we study an extremal problem concerning best approximation in the Hardy space $H^{1}$ on the unit disk $D$ . Specifically, we consider weighted combinations of…

math.CV2021

Fejér-type positive operator based on Takenaka--Malmquist system on unit circle

F. G. Abdullayev, V. V. Savchuk

Let $φ = {φ_{k}}_{k = - \infty}^{\infty}$ denote the extended Takenaka--Malmquist system on unit circle $T$ and let $σ_{n, φ} (f),$ $f \in L^{1} (T)$ , be the Fejér-type operator…

math.CV2015

Faber Polynomials with common zero

Viktor Savchuk

We describe the two sets of meromorphic univalent functions in the class $Σ$ , for which the sequence of Faber polynomials ${F_{j}}_{j = 1}^{\infty}$ have the roots with following prop…