Approximative characteristics of the Nikol’skii – Besov classes of functions $S_{1, θ}^r B(\mathbb{R}^d)$ - Radchenko, O. Ya.; Yanchenko, S. Ya. (Ukrains’kyi Matematychnyi Zhurnal, 2026)
UDC 517.51 We establish the exact-order estimates for the approximation of the classes $S^{\boldsymbol{r}}_{1,θ}B \left(\mathbb{R}^d\right)$ by entire functions of exponential type with supports of their Fourier transforms lying in a step hyperbolic cross.The error of approximation is estimated in the metric of the Lebesgue space $L_q\left(\mathbb{R}^d\right),\; 1 < q ≤ ∞.$