2019
Том 71
№ 11

All Issues

On the best polynomial approximation of entire transcendental functions in Banach spaces. II

Vakarchuk S. B.

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Abstract

We study the behavior of the best approximations $E_n(f)_{E′_p}$ of entire transcendental functions $f(z)$ of the order $ρ = 0$ by polynomials of at most $n$ th degree in the metric of the space $E′_p(Ω),\, p ≥ 1$. In particular, we describe the relationship between the best approximations $E_n(f)E′_p$ and the logarithmic order $ρ_L$ and type $σ_L$ of the function $f(z)$.

English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 10, pp 1451-1456.

Citation Example: Vakarchuk S. B. On the best polynomial approximation of entire transcendental functions in Banach spaces. II // Ukr. Mat. Zh. - 1994. - 46, № 10. - pp. 1318–1322.

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