Best approximation-preserving operators over Hardy space

Fahreddin ABDULLAYEV

Let Tn be the linear Hadamard convolution operator acting over Hardy space Hq, 1≤q≤∞. We call Tn a best approximation-preserving operator (BAP operator) if Tn(en)=en, where en(z):=zn, and if ∥Tn(f)∥q≤En(f)q for all f∈Hq, where En(f)q is the best approximation by algebraic polynomials of degree a most n−1 in Hq space. We give necessary and sufficient conditions for Tn to be a BAP operator over H∞. We apply this result to establish an exact lower bound for the best approximation of bounded holomorphic functions. In particular, we show that the Landau-type inequality ∣∣fˆn∣∣+c∣∣fˆN∣∣≤En(f)∞, wher ...Более

Статья 2023 Fen Fakültesi Analysis and Mathematical Physics13 ( 4 ) 31 Просмотры

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.

Статья 2021 Fen Fakültesi Analysis and Mathematical Physics11 ( 1 ) 72 Просмотры

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Best approximation-preserving operators over Hardy space

Fahreddin ABDULLAYEV

Faber polynomials with common zero

Fahreddin ABDULLAYEV | Meerim İmaş Kızı