On the Best Polynomial Approximations of Entire Transcendental Functions of Many Complex Variables in Some Banach Spaces

Abstract

For the entire transcendental functions $f$ of many complex variables $m (m ≥ 2)$ of finite generalized order of growth $ρ_m (f; α, β)$, we obtain the limiting relations between the indicated characteristic of growth and the sequences of best polynomial approximations of $f$ in the Hardy Banach spaces $H q (U^m )$ and in the Banach spaces $Bm(p, q, ⋋)$ studied by Gvaradze. The presented results are extensions of the corresponding assertions made by Varga, Batyrev, Shah, Reddy, Ibragimov, and Shikhaliev to the multidimensional case.