Approximation of Functions of Many Variables from the Classes $B_{p,θ}^{Ω} (ℝ^d)$ By Entire Functions of Exponential Type

Abstract

We obtain the decomposition representation of the norm of functions of many variables from the spaces $B_{p,θ}^{Ω} (ℝ^d)$ and establish the exact order estimates for the approximations of functions from the unit balls of these spaces by entire functions of exponential type in the space $L_q (ℝ^d)$.