On the Best Polynomial Approximations of Entire Transcendental Functions of Many Complex Variables in Some Banach Spaces
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.
English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 12, pp 1793-1811.
Citation Example: Vakarchuk S. B., Zhir S. I. On the Best Polynomial Approximations of Entire Transcendental Functions of Many Complex Variables in Some Banach Spaces // Ukr. Mat. Zh. - 2014. - 66, № 12. - pp. 1598–1614.