On the Best Polynomial Approximations of Entire Transcendental Functions of Many Complex Variables in Some Banach Spaces - Vakarchuk, S. B.; Zhir, S. I. (Ukrains’kyi Matematychnyi Zhurnal, 2014)
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.