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

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 $f(z)$.