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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 12, pp. 1598–1614, December, 2014.
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Vakarchuk, S.B., Zhir, S.I. On the Best Polynomial Approximations of Entire Transcendental Functions of Many Complex Variables in Some Banach Spaces. Ukr Math J 66, 1793–1811 (2015). https://doi.org/10.1007/s11253-015-1052-x
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DOI: https://doi.org/10.1007/s11253-015-1052-x