2017
Том 69
№ 6

All Issues

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

Vakarchuk S. B., Zhir S. I.


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.

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.